What is the extreme f(x)=x^3-3/2 x^2-6x+1 ?

The extreme f(x)=x^3-3/2 x^2-6x+1 is Maximum(-1, 9/2),Minimum(2,-9)

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extreme f(x)=x^3-3/2 x^2-6x+1

extreme points

f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x + 1

Maximum (- 1, \frac{9}{2}), Minimum (2, - 9)

Solution steps

f^{'} (x) = 3 x^{2} - 3 x - 6

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

x^{3} - \frac{3}{2} x^{2} - 6 x + 1 : \frac{9}{2}

Maximum (- 1, \frac{9}{2})

Plug

x = 2

into

x^{3} - \frac{3}{2} x^{2} - 6 x + 1 : - 9

Minimum (2, - 9)

Maximum (- 1, \frac{9}{2}), Minimum (2, - 9)

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

f (x) = 600 + 35 x

f (x) = 3 cos (π x), 0 \leq x \leq \frac{1}{6}

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

f (x) = \frac{1}{2} x^{\frac{2}{3}} - x^{\frac{1}{3}} + 3

What is the extreme f(x)=x^3-3/2 x^2-6x+1 ?
The extreme f(x)=x^3-3/2 x^2-6x+1 is Maximum(-1, 9/2),Minimum(2,-9)