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

The extreme f(x)=-5x^3-4x^4 is Maximum(-15/16 , 16875/16384),Saddle(0,0)

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

extreme

Maximum (- \frac{15}{16}, \frac{16875}{16384}), Saddle (0, 0)

Solution steps

f^{'} (x) = - 15 x^{2} - 16 x^{3}

Find intervals:

Increasing

: - \infty < x < - \frac{15}{16},

Decreasing

: - \frac{15}{16} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{15}{16}

into

- 5 x^{3} - 4 x^{4} : \frac{16875}{16384}

Maximum (- \frac{15}{16}, \frac{16875}{16384})

Plug

x = 0

into

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

Saddle (0, 0)

Maximum (- \frac{15}{16}, \frac{16875}{16384}), Saddle (0, 0)

What is the extreme f(x)=-5x^3-4x^4 ?
The extreme f(x)=-5x^3-4x^4 is Maximum(-15/16 , 16875/16384),Saddle(0,0)