What is the extreme f(x)=-5x^3+15x+7 ?

The extreme f(x)=-5x^3+15x+7 is Minimum(-1,-3),Maximum(1,17)

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extreme f(x)=-5x^3+15x+7

extreme points

f (x) = - 5 x^{3} + 15 x + 7

Minimum (- 1, - 3), Maximum (1, 17)

Solution steps

f^{'} (x) = - 15 x^{2} + 15

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- 5 x^{3} + 15 x + 7 : - 3

Minimum (- 1, - 3)

Plug

x = 1

into

- 5 x^{3} + 15 x + 7 : 17

Maximum (1, 17)

Minimum (- 1, - 3), Maximum (1, 17)

y = \frac{1}{3} x + 1

\frac{2 x ^{2} + 2 x}{- 3 x ^{2} - 18 x - 15}

f (x) = \frac{8 x ^{2} - 8}{3 x}

f (x) = 1 + (6 + x)^{\frac{1}{2}}

- 6 x

What is the extreme f(x)=-5x^3+15x+7 ?
The extreme f(x)=-5x^3+15x+7 is Minimum(-1,-3),Maximum(1,17)