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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 0 < x < \infty

Plug

x = - \frac{15}{16}

into

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

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

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- \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 Minimum(-15/16 ,-16875/16384),Saddle(0,0)