What is the extreme f(x)= 3/4 x^4-3x^3-81x^2-16 ?

The extreme f(x)= 3/4 x^4-3x^3-81x^2-16 is Minimum(-6,-1312),Maximum(0,-16),Minimum(9,-15373/4)

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extreme f(x)= 3/4 x^4-3x^3-81x^2-16

extreme points

f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16

Minimum (- 6, - 1312), Maximum (0, - 16), Minimum (9, - \frac{15373}{4})

Solution steps

f^{'} (x) = 3 x^{3} - 9 x^{2} - 162 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = - 6

into

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - 1312

Minimum (- 6, - 1312)

Plug

x = 0

into

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - 16

Maximum (0, - 16)

Plug

x = 9

into

\frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16 : - \frac{15373}{4}

Minimum (9, - \frac{15373}{4})

Minimum (- 6, - 1312), Maximum (0, - 16), Minimum (9, - \frac{15373}{4})

What is the extreme f(x)= 3/4 x^4-3x^3-81x^2-16 ?
The extreme f(x)= 3/4 x^4-3x^3-81x^2-16 is Minimum(-6,-1312),Maximum(0,-16),Minimum(9,-15373/4)