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

The extreme f(x)=-5x^4-5x^3-2 is Maximum(-3/4 ,-377/256),Saddle(0,-2)

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

extreme

Maximum (- \frac{3}{4}, - \frac{377}{256}), Saddle (0, - 2)

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} - 2 : - \frac{377}{256}

Maximum (- \frac{3}{4}, - \frac{377}{256})

Plug

x = 0

into

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

Saddle (0, - 2)

Maximum (- \frac{3}{4}, - \frac{377}{256}), Saddle (0, - 2)

What is the extreme f(x)=-5x^4-5x^3-2 ?
The extreme f(x)=-5x^4-5x^3-2 is Maximum(-3/4 ,-377/256),Saddle(0,-2)