Let f(x) = x (x- 4).(a) Find the critical numbers of the function f. (Enter your answers from smnallest to largest.)smallest valueX, =largest value(b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers?At x, the second derivative testSelect-At X2the second derivative testSelect-At x the second derivative testSelect-(c) What does the First Derivative Test tell you? Note what the First Derivative Test tells you that Second Derivative Test does noAt x, the first derivative testSelect-At x, the first derivative testSelect-At x, the first derivative testSelect--DETAILSSCALCET9M 4.7.025.

Answered: Image /qna-images/answer/47124d91-a2c5-43b9-8238-d1dbb6b1657b.jpg

Answered: Let f(x) = x(x-4). (a) Find 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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Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in exact form.
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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?
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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
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)
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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. f(x) = x2 − 4x + 1 f has a relative minimum at the critical point x =_____________________
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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

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