Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 4 - 10 Step 1 The minimum and maximum of a function on an interval are the extreme values, or extrema (the singular form of extrema is extremum), of the function on the interval. In the given problem, the extremum occurs when x = 3 The specified function is f(x) = -3xx + 2 = -3x(x + 2)1/2 Differentiate f(x) using the product rule. f "(x) = -3x (x + 2) J + (x + 2)1/2. ([

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 7CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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Find the value of the derivative (if it exists) at the indicated extremum.
-4 4V6
f(x) = - 3xVx + 2
10
5
-2
2
4
–5
- 10
Step 1
The minimum and maximum of a function on an interval are the extreme values, or extrema (the singular form of extrema is extremum), of the function on the interval. In the given problem, the
extremum occurs when x =
The specified function is f(x) = -3xx + 2 = -3x(x + 2)1/2.
Differentiate f(x) using the product rule.
x[C
+ 2)1/2 . ([
f '(x) = -3
(x + 2)
+ (x
Transcribed Image Text:Find the value of the derivative (if it exists) at the indicated extremum. -4 4V6 f(x) = - 3xVx + 2 10 5 -2 2 4 –5 - 10 Step 1 The minimum and maximum of a function on an interval are the extreme values, or extrema (the singular form of extrema is extremum), of the function on the interval. In the given problem, the extremum occurs when x = The specified function is f(x) = -3xx + 2 = -3x(x + 2)1/2. Differentiate f(x) using the product rule. x[C + 2)1/2 . ([ f '(x) = -3 (x + 2) + (x
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