Check the solution to "Use the first derivatives test to find local..."

Daniell Phillips

Answered question

2021-12-10

Use the first derivatives test to find local exterma of

f (x) = x^{3} - 12 x

on R

Raymond Foley

Beginner2021-12-11Added 39 answers

Step 1
We have to use the first derivative test to find the local exterma
The given expression is

f (x) = x^{3} - 12 x

Step 2
we have

f (x) = x^{3} - 12 x

differentiate with respect to x

f^{'} (x) = 3 x^{2} - 12

put f'(X)=0

3 x^{2} - 12 = 0

divide by 3 on both sides

x^{2} - 4 = 0

x^{2} - 2^{2} = 0

(x+2)(x-2)=0
x=2 OR x=-2
Step 3
So, we have local minima at x=2
put x=2 in f(x)

f (2) = 2^{3} - 12 \cdot 2

f(2)=8-24=-16
local minima at x=2 is -16
We have local maxima at x=-2
put x=-2 in f(x)

f (2) = - 2^{3} - 12 \cdot (- 2)

f(2)=-8+24=16
Local maxima at x=-2 is 16

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