Consider the function below.f(x) = -4x2 + 8x + 9(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)(b) Find the open intervals on which the function is increasing ordecreasing. (Enter your answer using interval notation. If an answerdoes not exist, enter DNE.)(-0, 3)increasing(3, 0)decreasing(c) Apply the First Derivative Test to identify the relative extrema. (If ananswer does not exist, enter DNE.)dne(х, у) %3Drelative minimumх)3, 13(х, у) %3Drelative maximum

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Asked Feb 6, 2020
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Consider the function below.
f(x) = -4x2 + 8x + 9
(a) Find the critical numbers of f. (Enter your answers as a comma-
separated list.)
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answer using interval notation. If an answer
does not exist, enter DNE.)
(-0, 3)
increasing
(3, 0)
decreasing
(c) Apply the First Derivative Test to identify the relative extrema. (If an
answer does not exist, enter DNE.)
dne
(х, у) %3D
relative minimum
х)
3, 13
(х, у) %3D
relative maximum
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Consider the function below. f(x) = -4x2 + 8x + 9 (a) Find the critical numbers of f. (Enter your answers as a comma- separated list.) (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (-0, 3) increasing (3, 0) decreasing (c) Apply the First Derivative Test to identify the relative extrema. (If an answer does not exist, enter DNE.) dne (х, у) %3D relative minimum х) 3, 13 (х, у) %3D relative maximum

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Expert Answer

Step 1

Given,

Calculus homework question answer, step 1, image 1
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Step 2

a). Critical numbers are the values of x for which first derivative is zero.

 So, we find the derivative of f(x), that is

Calculus homework question answer, step 2, image 1
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Step 3

b). A function increases if its first derivative is positive and ...

Calculus homework question answer, step 3, image 1
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