Question
Asked Oct 10, 2019
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Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

h(x) = 9(x − 7)3
relative maximum     (x, y)  = 
 
 
 
 
 
 
 
relative minimum     (x, y)  = 
 
 
 
 
 
 
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Expert Answer

Step 1

Given: -

h(x) — 9(х- 7)°
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h(x) — 9(х- 7)°

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Step 2

To find: -

a) Relative maximum
b) Relative minimum
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a) Relative maximum b) Relative minimum

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Step 3

Calculation...

It is given that
h(x) 9(x-7
The first derivative of h(x)
h(x)9x3(x-7)
27(x-7)2
Putting
h'(x) 0
27(x-7)2 0
x-7 0
x 7
Finding the second derivative of h(x)
h"(x) = 27x2 x (x-7)
54(x-7)
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It is given that h(x) 9(x-7 The first derivative of h(x) h(x)9x3(x-7) 27(x-7)2 Putting h'(x) 0 27(x-7)2 0 x-7 0 x 7 Finding the second derivative of h(x) h"(x) = 27x2 x (x-7) 54(x-7)

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Tagged in

Math

Calculus

Derivative