1. Let f(x) = 3x¹ - 4x³-12x².(a) Find all critical numbers for the function f.(b) Determine all those intervals on which the graph of f is increasing and all those onwhich it is decreasing by analyzing the sign of the derivative function.(c) Find and classify all of the relative extreme values/points by applying the FirstDerivative Test.(d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c).(e) Indicate any absolute maximum or minimum values that exist for this function f.

Let fx=3x4-4x3-12x2 (a) To find all critical numbers for the function f. (b) To determine all those…

Answered: 1. Let f(x)= 3x² - 4x³ - 12x². (a) Find…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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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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