What is the extreme f(x)=4x^3+3x^2-60x-12 ?

The extreme f(x)=4x^3+3x^2-60x-12 is Maximum(-5/2 , 377/4),Minimum(2,-88)

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extreme f(x)=4x^3+3x^2-60x-12

extreme points

f (x) = 4 x^{3} + 3 x^{2} - 60 x - 12

Maximum (- \frac{5}{2}, \frac{377}{4}), Minimum (2, - 88)

Solution steps

f^{'} (x) = 12 x^{2} + 6 x - 60

Find intervals:

Increasing

: - \infty < x < - \frac{5}{2},

Decreasing

: - \frac{5}{2} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{5}{2}

into

4 x^{3} + 3 x^{2} - 60 x - 12 : \frac{377}{4}

Maximum (- \frac{5}{2}, \frac{377}{4})

Plug

x = 2

into

4 x^{3} + 3 x^{2} - 60 x - 12 : - 88

Minimum (2, - 88)

Maximum (- \frac{5}{2}, \frac{377}{4}), Minimum (2, - 88)

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

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

f (x) = 4 x e^{- x}

f (x) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

f (x, y) = 4 x^{4} + y^{2} - 2 x y + 1

What is the extreme f(x)=4x^3+3x^2-60x-12 ?
The extreme f(x)=4x^3+3x^2-60x-12 is Maximum(-5/2 , 377/4),Minimum(2,-88)