What is the extreme f(x)=5x^4+5x^3+7 ?

The extreme f(x)=5x^4+5x^3+7 is Minimum(-3/4 , 1657/256),Saddle(0,7)

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extreme f(x)=5x^4+5x^3+7

extreme points

f (x) = 5 x^{4} + 5 x^{3} + 7

Minimum (- \frac{3}{4}, \frac{1657}{256}), Saddle (0, 7)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{4}

into

5 x^{4} + 5 x^{3} + 7 : \frac{1657}{256}

Minimum (- \frac{3}{4}, \frac{1657}{256})

Plug

x = 0

into

5 x^{4} + 5 x^{3} + 7 : 7

Saddle (0, 7)

Minimum (- \frac{3}{4}, \frac{1657}{256}), Saddle (0, 7)

What is the extreme f(x)=5x^4+5x^3+7 ?
The extreme f(x)=5x^4+5x^3+7 is Minimum(-3/4 , 1657/256),Saddle(0,7)