What is the extreme f(x)=-4x^3-6x^2+72x+6 ?

The extreme f(x)=-4x^3-6x^2+72x+6 is Minimum(-3,-156),Maximum(2,94)

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extreme f(x)=-4x^3-6x^2+72x+6

extreme points

f (x) = - 4 x^{3} - 6 x^{2} + 72 x + 6

Minimum (- 3, - 156), Maximum (2, 94)

Solution steps

f^{'} (x) = - 12 x^{2} - 12 x + 72

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 3

into

- 4 x^{3} - 6 x^{2} + 72 x + 6 : - 156

Minimum (- 3, - 156)

Plug

x = 2

into

- 4 x^{3} - 6 x^{2} + 72 x + 6 : 94

Maximum (2, 94)

Minimum (- 3, - 156), Maximum (2, 94)

y = 12 x^{\frac{5}{7}} + 5 x^{\frac{12}{7}}

y = x^{3} - 3 x^{2} + 7 x - 10

f (x) = - \frac{10}{3} x^{3} - \frac{31}{2} x^{2} - 3 x + 4

f (x) = \frac{x ^{2} + 7 x + 13}{x + 4}

\frac{( 5 x - 8 )}{x}

What is the extreme f(x)=-4x^3-6x^2+72x+6 ?
The extreme f(x)=-4x^3-6x^2+72x+6 is Minimum(-3,-156),Maximum(2,94)