(a) Find the critical numbers of the function f(x) = x(x - 1)5.(smallest value)X =X=X =(b) What does the Second Derivative Test tell you about the behavior off at these critical numbers?At x =the function has ---Select---At x =(largest value)(c) What does the First Derivative Test tell you? (Enter your answers from smallest to largest x value.)the function has ---Select---the function has ---Select---the function has ---Select---At x =At x =I1

NOTE: Refresh your page if you can't see any equations. . take derivative factor out

Answered: (a) Find the critical numbers of the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer.B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.C. Find the value of f(-1).
Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in exact form.
2. Find all critical values, local extrema and the absolute maximum and absolute minimum values of f(x)= x(4-x)2 on the interval [0,5].
a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = √x ln x on (0, ∞)
Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical points does this function have? Where are they located on the x-axis? Does ƒ have an absolute minimum? An absolute maximum?
1) Use the First Derivative Test to determine whether the function attains a local minimum or local maximum (or neither) at the given critical point y=x2/x+1, c=0 1a) find the critical points and the intervals on which the function is increasing or decreasing, and apply the First Derivative Test to each critical point y=x5/2-x2 (x>0)
Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and b
Find the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x) = x3 − 3x + 5 g has a relative maximum at the critical point x =________ (Smaller x-value) g has a relative minimum at the critical point x =____________(larger x-value)
Find the critical numbers of f(x) = x4(x-1)3 A. What does the second derivative test tell you about the behavior of f at these critical numbers? B. What does the first derivative test tell you?
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
Find the X coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, relative minimum, or neither by first applying the second derivative test, and, if the test fails, by some other method. g(x)=3x^3-9x+9 (a) g has a relative maximum at the critical point X=_____(smaller x value) (b) g has a relative minimum at the critical point X=_____(larger x value)
1. Find all critical values, local extrema and the absolute maximum and absolute minimum values of F(x)=X3-12x on the interval [-1,3]. 2. Find all critical values, local extrema and the absolute maximum and absolute minimum values of f(x)= x(4-x)2 on the interval [0,5].

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