What is the extreme f(x)= 2/5 x^5+5x^4+16x^3-15 ?

The extreme f(x)= 2/5 x^5+5x^4+16x^3-15 is Maximum(-6,-507/5),Minimum(-4,-843/5),Saddle(0,-15)

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extreme f(x)= 2/5 x^5+5x^4+16x^3-15

extreme points

f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Saddle (0, - 15)

Solution steps

f^{'} (x) = 2 x^{4} + 20 x^{3} + 48 x^{2}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{507}{5}

Maximum (- 6, - \frac{507}{5})

Plug

x = - 4

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{843}{5}

Minimum (- 4, - \frac{843}{5})

Plug

x = 0

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - 15

Saddle (0, - 15)

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Saddle (0, - 15)

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

f (x, y) = x^{2} + y^{2} - 2 x - 6 y + 14

f (x, y) = x^{3} - y^{3} - 2 x y + 6

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

f (t) = 2 x

What is the extreme f(x)= 2/5 x^5+5x^4+16x^3-15 ?
The extreme f(x)= 2/5 x^5+5x^4+16x^3-15 is Maximum(-6,-507/5),Minimum(-4,-843/5),Saddle(0,-15)