What is the extreme f(x)=375t-5t^3 ?

The extreme f(x)=375t-5t^3 is Minimum(-5,-1250),Maximum(5,1250)

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extreme f(x)=375t-5t^3

extreme points

f (x) = 375 t - 5 t^{3}

Minimum (- 5, - 1250), Maximum (5, 1250)

Solution steps

f^{'} (t) = 375 - 15 t^{2}

Find intervals:

Decreasing

: - \infty < t < - 5,

Increasing

: - 5 < t < 5,

Decreasing

: 5 < t < \infty

Plug

t = - 5

into

375 t - 5 t^{3} : - 1250

Minimum (- 5, - 1250)

Plug

t = 5

into

375 t - 5 t^{3} : 1250

Maximum (5, 1250)

Minimum (- 5, - 1250), Maximum (5, 1250)

f (x, y) = x^{3} - y^{3} + 3 x y

f (x) = x^{3} + 1, 1 \leq x \leq 2

f (x) = x (125 - x)^{2}

f (x) = e^{8 x^{2} + 10 y^{2} + 6}

f (x) = - (x - 1)^{2} + 10

What is the extreme f(x)=375t-5t^3 ?
The extreme f(x)=375t-5t^3 is Minimum(-5,-1250),Maximum(5,1250)