What is the extreme f(x)=-5x^4-5x^3+29 ?

The extreme f(x)=-5x^4-5x^3+29 is Maximum(-3/4 , 7559/256),Saddle(0,29)

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extreme f(x)=-5x^4-5x^3+29

extreme points

f (x) = - 5 x^{4} - 5 x^{3} + 29

Maximum (- \frac{3}{4}, \frac{7559}{256}), Saddle (0, 29)

Solution steps

f^{'} (x) = - 20 x^{3} - 15 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{4},

Decreasing

: - \frac{3}{4} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{3}{4}

into

- 5 x^{4} - 5 x^{3} + 29 : \frac{7559}{256}

Maximum (- \frac{3}{4}, \frac{7559}{256})

Plug

x = 0

into

- 5 x^{4} - 5 x^{3} + 29 : 29

Saddle (0, 29)

Maximum (- \frac{3}{4}, \frac{7559}{256}), Saddle (0, 29)

What is the extreme f(x)=-5x^4-5x^3+29 ?
The extreme f(x)=-5x^4-5x^3+29 is Maximum(-3/4 , 7559/256),Saddle(0,29)