maximumminimum The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use thesecond derivative test to classify them.f(x) has a localat the smaller critical point c₁sinc ✔f''(c1)>0f" (c1) >0f(x) has a localat the larger critical point c2f''(c1) <0f" (c1) <0since

We need to find and classify critical points.

Answered: The function f(x) = −2x³+3x²+36x has…

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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3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a) Find f"(x). (b) Then use the second derivative test to identify the critical point as eithera local minimum, a local maximum, or neither.
A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.
Given the function f(x)=x4-6x2-60x2+134x+30 The value x=1 satisfies the equation f'(x)=0 (that is, x=1 is a critical value). Determine if f(x) has a local maximum or minimum at x=1 by using the second derivative test.
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
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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The function f(x) = −2x³+3x²+36x has two critical points, c₁ and c₂. Find them and use the second derivative test to classify them. f(x) has a local at the smaller critical point c₁ sinc f(x) has a local at the larger critical point c2 f''(c1)>0f" (c1)>0 f''(c1) <0f" (c1) <0 since