Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 - 9x2 - 216x + 2, [-4, 5] Step 1 The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an endpoint of the interval. Recall that a critical point is a point where f '(x) = 0 or is undefined. We begin by finding the derivative of f. f "(x) = 18x2 – 18x – 216 v 182 – 18r – 216| Step 2 We now solve f '(x) = 0 for x, which gives the following critical numbers. (Enter your answers as a comma- separated list.) = -3,4 -3, 4 Step 3 We must now find the function values at the critical numbers we just found and at the endpoints of the interval [-4, 5). f(-3) = 45 f(4) = f(-4) = f(5) =
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 - 9x2 - 216x + 2, [-4, 5] Step 1 The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an endpoint of the interval. Recall that a critical point is a point where f '(x) = 0 or is undefined. We begin by finding the derivative of f. f "(x) = 18x2 – 18x – 216 v 182 – 18r – 216| Step 2 We now solve f '(x) = 0 for x, which gives the following critical numbers. (Enter your answers as a comma- separated list.) = -3,4 -3, 4 Step 3 We must now find the function values at the critical numbers we just found and at the endpoints of the interval [-4, 5). f(-3) = 45 f(4) = f(-4) = f(5) =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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how to solve for the critical numbers please
![Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 6x3 – 9x² – 216x + 2,
[-4, 5]
Step 1
The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an
endpoint of the interval. Recall that a critical point is a point where f '(x) = 0 or is undefined. We begin by
finding the derivative of f.
f '(x) = 18x – 18x – 216
18x2
1822 – 18x – 216
Step 2
We now solve f '(x) = 0 for x, which gives the following critical numbers. (Enter your answers as a comma-
separated list.)
X =
|-3,4
-3, 4
Step 3
We must now find the function values at the critical numbers we just found and at the endpoints of the
interval [-4, 5].
f(-3) = 45
f(4)
f(-4)
f(5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa699feee-67df-45a7-b712-d93645cac786%2F75e4e929-ad40-41d4-b5c8-98bdf3eb5f38%2Fctg7xe_processed.png&w=3840&q=75)
Transcribed Image Text:Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 6x3 – 9x² – 216x + 2,
[-4, 5]
Step 1
The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an
endpoint of the interval. Recall that a critical point is a point where f '(x) = 0 or is undefined. We begin by
finding the derivative of f.
f '(x) = 18x – 18x – 216
18x2
1822 – 18x – 216
Step 2
We now solve f '(x) = 0 for x, which gives the following critical numbers. (Enter your answers as a comma-
separated list.)
X =
|-3,4
-3, 4
Step 3
We must now find the function values at the critical numbers we just found and at the endpoints of the
interval [-4, 5].
f(-3) = 45
f(4)
f(-4)
f(5)
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