What is the extreme f(x)=-x^3+15x^2+13 ?

The extreme f(x)=-x^3+15x^2+13 is Minimum(0,13),Maximum(10,513)

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extreme f(x)=-x^3+15x^2+13

extreme points

f (x) = - x^{3} + 15 x^{2} + 13

Minimum (0, 13), Maximum (10, 513)

Solution steps

f^{'} (x) = - 3 x^{2} + 30 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = 0

into

- x^{3} + 15 x^{2} + 13 : 13

Minimum (0, 13)

Plug

x = 10

into

- x^{3} + 15 x^{2} + 13 : 513

Maximum (10, 513)

Minimum (0, 13), Maximum (10, 513)

x^{\frac{1}{3}} (x^{2} - 9), - 4 \leq x \leq 2

f (x) = x e^{- x^{2}} [0.2]

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 6

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 8

- 6 x + x^{2}

What is the extreme f(x)=-x^3+15x^2+13 ?
The extreme f(x)=-x^3+15x^2+13 is Minimum(0,13),Maximum(10,513)