What is the critical f(x)=(x-4)(x/2+1)^3 ?

The critical f(x)=(x-4)(x/2+1)^3 is x=-2,x\approx-1.99999…,x\approx 2.50000…

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critical f(x)=(x-4)(x/2+1)^3

critical points

f (x) = (x - 4) (\frac{x}{2} + 1)^{3}

x = - 2, x \approx - 1.99999 \dots, x \approx 2.50000 \dots

Solution steps

(x - 4) (\frac{x}{2} + 1)^{3}

Find where

f^{'} (x)

is equal to zero or undefined

x = - 2, x \approx - 1.99999 \dots, x \approx 2.50000 \dots

Identify critical points not in

f (x)

domain

Domain of

(x - 4) (\frac{x}{2} + 1)^{3} : - \infty < x < \infty

All critical points are in domain

x = - 2, x \approx - 1.99999 \dots, x \approx 2.50000 \dots

\frac{x - 4}{2 x - 12}

(- 3, 5), (- 7, - 9)

f (x) = 3 x^{3} - 1

2 cos (x)

f (x) = \frac{x ^{2} - 1}{x - 2}

What is the critical f(x)=(x-4)(x/2+1)^3 ?
The critical f(x)=(x-4)(x/2+1)^3 is x=-2,x\approx-1.99999…,x\approx 2.50000…