{ "cells": [ { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "# remember to include these two lines of code at the start of your document!\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = \"all\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MATH1110 Lab 6: Critical and Inflection Points\n", "\n", "Good to see you again!" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = var('x, y')\n", "one = implicit_plot(cos(x-y)==x, (x, -2, 4), (y, 0, 6), color = 'black')\n", "two = implicit_plot(sin(-y/3-2)==x, (x, 0, 4), (y, 6, 10), color = 'black')\n", "three = implicit_plot(log(9*x-6)+10==y, (x, 0, 4), (y, 10, 15), color = 'black')\n", "four = implicit_plot(-abs(2*y+3)+3==x, (x, 1/2, 3), (y, -4, 3), color = 'black')\n", "five = implicit_plot(-ln(5*x-2)-4==y, (x, 1/5, 3), (y, -6, -3), color = 'black')\n", "six = points([[0, -3/2], [-3, -3/2], [-6, -3/2], [-9, -3/2]], size = 25,\\\n", " color = 'orange')\n", "seven = text('~~ Happy ~~', (-4, 9), color = 'black', fontsize = 10 )\n", "eight = text('Halloween', (-4, 7.5), color = 'orange', fontsize = 15 )\n", "show(one+two+three+four+five+six+seven+eight)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Objectives for today:**\n", "\n", "1. What have we done with Sage so far?\n", "2. Critical points\n", "3. Inflection points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. What we've done so far" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a refersher, here's what we've done with Sage so far.\n", "\n", "* Defining variables, building different kinds of functions\n", "* Plotting, layering plots, making plots fancy\n", "* Implicitly defined plots\n", "* Limits\n", "* Different uses of the *solve* command\n", "* Derivatives\n", "* Differential equations, initial value problems\n", "* Identifying and solving errors\n", "\n", "If you're feeling really lost on any of this content, please reach out to Maya or Stefan either in office hours or by email (sbilaniuk@trentu.ca, mapeters@trentu.ca)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Critical points\n", "\n", "What is a critical point?\n", "\n", "Critical points include maximums and minimums - places where the slope of our function switches from negative to positive or positive to negative. That is where the derivative of a function equals zero." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "t" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('t')\n", "q = sin(t)/(4*t)\n", "func = plot( q, t, -10, 10, color = 'navy', thickness = 2)\n", "dfunc = plot( diff(q, t), t, -10, 10, color = 'dodgerblue')\n", "func+dfunc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the visualization above, we can see the navy blue maximum and minimum points correspond with where the lighter blue derivative function crosses the x-axis. What does the derivative being above or below the x-axis tell us about the original navy blue function?\n", "\n", "Let's take the cubic function $y=\\frac{x^3}{7}-2x+2$.\n", "We can use the *solve(\\_)* command to locate these critical points by creating an equation where our first derivative equal to zero. In the second argument, we are solving for $x$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x=var('x')\n", "y=x^3/7-2*x+2\n", "plot(y, x, -5, 5, color = 'crimson')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sage has another helpful command we can use to identify critical points. A \"root\" is a spot where a function passes across the x-axis. The command *find_root(\\_)* requires the function (not equation) we want the root of, and then the lower and upper bound of a domain within which we expect to find a root. Before using this function, it's very helpful to have a plot of your function to know where you're looking.\n", "\n", "Plot $y(x)$ with its quadratic derivative after finding the roots of the derivative function. Notice how $y(x)$ is increasing whenever $y'(x)$ is positive and decreasing when $y'(x)$ is negative." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise question\n", "1. Plot $g(x) = \\large{ 2^{\\left(\\frac{x}{3}\\right)}\\sin{(x)} }$ with its derivative on the domain [-5, 3]. Find all the local maximums and minimums of the function within this region." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Inflection points\n", "\n", "While the first derivative pertains to slope, the second derivative informs us on *concavity*. Concavity can be remembered as whether the curve is in a frowning (\"concave down\") or smiling (\"concave up\") arc, and the points of transition between the two are called infection points.\n", "\n", "Some observations from the graph below:\n", "* The orange curve (second derivative) crossing the x-axis shows when we have a change in concavity in the original function.\n", "* The navy blue curve is concave down in the same regions where the orange curve is negative.\n", "* The navy blue curve is concave up in the same regions where the orange curve is positive.\n", "* Maximums and minimums of the light blue curve (first derivative) are where the orange curve crosses the x-axis." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clear_vars()\n", "var('t')\n", "q = sin(t)/(4*t)\n", "func = plot( q, t, -10, 10, color = 'navy', thickness = 2)\n", "dfunc = plot( diff(q, t), t, -10, 10, color = 'dodgerblue')\n", "d2func = plot( diff(q, t, 2), t, -10, 10, color = 'orange', thickness = 2)\n", "func+dfunc+d2func" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If a function is smooth and continuous (differentiable across its entire domain), there will be an inflection point between every max and min.\n", "\n", "Returning to our cubic example, show the second derivative. How many critical points will there be and how do you know?\n", "Use Sage to find the coordinates of the inflection point(s). If using the *find_root(\\_)* method, remember to plot the function first so you know subregion of the domain where we are looking for an inflection point." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How are we doing? Is this making sense?\n", "\n", "### Exercise question\n", "2. Find all inflection points of $g(x) = \\large{ 2^{\\left(\\frac{x}{3}\\right)}\\sin{(x)} }$ (same function as the previous example question) and plot $g$ with the first and second derivative. Discuss in comments in your code how the increasing/decreasing behaviour and concavity of the original function are shown by the first and second derivative curves." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }