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13-15 Sketch the graph of a function that satisfies the given conditions.
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Calculus (MindTap Course List)
- (a) Use a graph to estimate the absolute maximum andminimum values of the function to two decimal places.(b) Use calculus to find the exact maximum and minimumvalues. f(x) =x √(x- x2)arrow_forward1. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f (x, y) = x2 + xy + y2 + 7yarrow_forward4(2) Show, and explain well your calculations. Please find: A) Image of the function given. B) Intervals where the g(x) function is positive or negative. C) Growth and decay intervals of the g(x) function. D) The intersection points of the affine function and its inverse.arrow_forward
- Even and odd functionsa. Suppose a nonconstant even function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An even function satisfies ƒ(-x) = ƒ(x).)b. Suppose a nonconstant odd function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An odd function satisfies ƒ(-x) = -ƒ(x).)arrow_forwardUse calculus to find the Global Maximum function value, and the Global minimum function value for the function f(x)=Ln(x2−4x+6) on the closed interval [0, 8] A) the Global Minimum is y=Ln(6) the Global Maximum is y=Ln(38) B) the Global Minimum is y=Ln(2) the Global Maximum is y=Ln(6) C) the Global Minimum is y=Ln(2) the Global is Maximum is y=Ln(38)arrow_forwardFind the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. f(x, y) = y2 − 2y cos x, −1 ≤ x ≤ 7arrow_forward
- EXAMPLE 6 The Heaviside function H is defined by [This function is named after the electrical engineer Oliver Heaviside (1850-1925) and can be used to describe an electric current that is switched on at time t = 0.] Its graph is shown in the figure.As t approaches 0 from the left, H(t) approaches . As t approaches 0 from the right, H(t) approaches . Therefore the limit as t approaches 0 of H(t) does not exist.arrow_forward(a) Use a graph to estimate the absolute maximum andminimum values of the function to two decimal places.(b) Use calculus to find the exact maximum and minimumvalues. f(x) = x4 - 3x3 +3x2 -x, 0 ≤ x ≤ 2arrow_forwardQuestion Number 1: Sketch the graph of the function defined piecewise by the formula f(x)={0,_<-1;sqrt(1-x^2),-1<x<1,x,x_>1. A positive number _ and the limit L of a function f at a are given. Find a number δ such that |f(x) − L| < _ if 0 < |x − a| < δ. limx to 3 (x^2 - 9) /(x-3) =6;E=0.05 Find an equation for the tangent line to the curve y = 2/x at the point (2, 1) on this curve.arrow_forward
- Need help with my practice question. Sketch the graph of a function with domain [−4, 2] that satisfies the following properties: it is continuous on the whole interval, it achieves its absolute maximum value at x = 2 and at x = −3, it achieves its absolute minimum value at x = −2, it has a local minimum at x = 1, it has a local maximum at x = −1, and it has a critical point that is neither a local minimum nor a local maximum at x = 0.arrow_forwardQ3-5. The function f has a local/relative minimum value when x = It has a local/relative maximum when x = The graph of f has an inflection point at x =arrow_forward(a) Sketch the graph of a function that has a local maximumat 2 and is differentiable at 2.(b) Sketch the graph of a function that has a local maximumat 2 and is continuous but not differentiable at 2.(c) Sketch the graph of a function that has a local maximumat 2 and is not continuous at 2.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning