What is the extreme f(x)=-x^3+6x^2+15x+4 ?

The extreme f(x)=-x^3+6x^2+15x+4 is Minimum(-1,-4),Maximum(5,104)

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extreme f(x)=-x^3+6x^2+15x+4

extreme points

f (x) = - x^{3} + 6 x^{2} + 15 x + 4

Minimum (- 1, - 4), Maximum (5, 104)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x + 15

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 1

into

- x^{3} + 6 x^{2} + 15 x + 4 : - 4

Minimum (- 1, - 4)

Plug

x = 5

into

- x^{3} + 6 x^{2} + 15 x + 4 : 104

Maximum (5, 104)

Minimum (- 1, - 4), Maximum (5, 104)

\frac{csc ( x )}{1 + csc ( x )}

f (x) = x^{\frac{8}{3}}, - 8 \leq x \leq 1

f (x) = - 2 sin^{2} (x), \frac{π}{4} \leq x \leq 2 π

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

f (x, y) = ln (x^{2} + 4 y^{2} - 4)

What is the extreme f(x)=-x^3+6x^2+15x+4 ?
The extreme f(x)=-x^3+6x^2+15x+4 is Minimum(-1,-4),Maximum(5,104)