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

The extreme f(x)=-5x^3-2x^4 is Maximum(-15/8 , 16875/2048),Saddle(0,0)

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extreme f(x)=-5x^3-2x^4

extreme points

f (x) = - 5 x^{3} - 2 x^{4}

Maximum (- \frac{15}{8}, \frac{16875}{2048}), Saddle (0, 0)

Solution steps

f^{'} (x) = - 15 x^{2} - 8 x^{3}

Find intervals:

Increasing

: - \infty < x < - \frac{15}{8},

Decreasing

: - \frac{15}{8} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{15}{8}

into

- 5 x^{3} - 2 x^{4} : \frac{16875}{2048}

Maximum (- \frac{15}{8}, \frac{16875}{2048})

Plug

x = 0

into

- 5 x^{3} - 2 x^{4} : 0

Saddle (0, 0)

Maximum (- \frac{15}{8}, \frac{16875}{2048}), Saddle (0, 0)

f (x) = 4 x + 9

\frac{4 - x}{( x + 1 ) ( x ^{2} + 1 )}

f (x) = (x + 20)^{2} - 30

y = 2 x - 4

What is the extreme f(x)=-5x^3-2x^4 ?
The extreme f(x)=-5x^3-2x^4 is Maximum(-15/8 , 16875/2048),Saddle(0,0)