What is the extreme f(x)= 3/4 x^4+15x^3+75x^2-23 ?

The extreme f(x)= 3/4 x^4+15x^3+75x^2-23 is Minimum(-10,-23),Maximum(-5, 1783/4),Minimum(0,-23)

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extreme f(x)= 3/4 x^4+15x^3+75x^2-23

extreme points

f (x) = \frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23

Minimum (- 10, - 23), Maximum (- 5, \frac{1783}{4}), Minimum (0, - 23)

Solution steps

f^{'} (x) = 3 x^{3} + 45 x^{2} + 150 x

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < - 5,

Decreasing

: - 5 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 10

into

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : - 23

Minimum (- 10, - 23)

Plug

x = - 5

into

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : \frac{1783}{4}

Maximum (- 5, \frac{1783}{4})

Plug

x = 0

into

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : - 23

Minimum (0, - 23)

Minimum (- 10, - 23), Maximum (- 5, \frac{1783}{4}), Minimum (0, - 23)

What is the extreme f(x)= 3/4 x^4+15x^3+75x^2-23 ?
The extreme f(x)= 3/4 x^4+15x^3+75x^2-23 is Minimum(-10,-23),Maximum(-5, 1783/4),Minimum(0,-23)