What is the extreme f(x)=15t+6t^2-t^3 ?

The extreme f(x)=15t+6t^2-t^3 is Minimum(-1,-8),Maximum(5,100)

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extreme f(x)=15t+6t^2-t^3

extreme points

f (x) = 15 t + 6 t^{2} - t^{3}

Minimum (- 1, - 8), Maximum (5, 100)

Solution steps

f^{'} (t) = 15 + 12 t - 3 t^{2}

Find intervals:

Decreasing

: - \infty < t < - 1,

Increasing

: - 1 < t < 5,

Decreasing

: 5 < t < \infty

Plug

t = - 1

into

15 t + 6 t^{2} - t^{3} : - 8

Minimum (- 1, - 8)

Plug

t = 5

into

15 t + 6 t^{2} - t^{3} : 100

Maximum (5, 100)

Minimum (- 1, - 8), Maximum (5, 100)

f (x) = \frac{x + 1}{x - 8}

f (x) = 6 x^{2} - x - 12

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

f (x) = \frac{3}{x - 1}

\frac{5 x - 10}{27 - 6 x}

What is the extreme f(x)=15t+6t^2-t^3 ?
The extreme f(x)=15t+6t^2-t^3 is Minimum(-1,-8),Maximum(5,100)