What is the extreme f(x)=-3x^4-7x^3+23 ?

The extreme f(x)=-3x^4-7x^3+23 is Maximum(-7/4 , 8289/256),Saddle(0,23)

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extreme f(x)=-3x^4-7x^3+23

extreme points

f (x) = - 3 x^{4} - 7 x^{3} + 23

Maximum (- \frac{7}{4}, \frac{8289}{256}), Saddle (0, 23)

Solution steps

f^{'} (x) = - 12 x^{3} - 21 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{7}{4},

Decreasing

: - \frac{7}{4} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{7}{4}

into

- 3 x^{4} - 7 x^{3} + 23 : \frac{8289}{256}

Maximum (- \frac{7}{4}, \frac{8289}{256})

Plug

x = 0

into

- 3 x^{4} - 7 x^{3} + 23 : 23

Saddle (0, 23)

Maximum (- \frac{7}{4}, \frac{8289}{256}), Saddle (0, 23)

What is the extreme f(x)=-3x^4-7x^3+23 ?
The extreme f(x)=-3x^4-7x^3+23 is Maximum(-7/4 , 8289/256),Saddle(0,23)