What is the extreme f(x)= 1/3 x^3+3/2 x^2-4x ?

The extreme f(x)= 1/3 x^3+3/2 x^2-4x is Maximum(-4, 56/3),Minimum(1,-13/6)

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extreme f(x)= 1/3 x^3+3/2 x^2-4x

extreme points

f (x) = \frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 4 x

Maximum (- 4, \frac{56}{3}), Minimum (1, - \frac{13}{6})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 4

into

\frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 4 x : \frac{56}{3}

Maximum (- 4, \frac{56}{3})

Plug

x = 1

into

\frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 4 x : - \frac{13}{6}

Minimum (1, - \frac{13}{6})

Maximum (- 4, \frac{56}{3}), Minimum (1, - \frac{13}{6})

\frac{d}{d x} ((x + y) 2 + 2 y^{2})

f (x) = \frac{2 ( x + 7 ) ^{2}}{x + 10}

\frac{2 x ^{2} - 5 x + 5}{x - 2}

f (x) = 2 x^{2} - 12 x + 20

f (x) = 4 sin^{2} (x), 0 \leq x \leq π

What is the extreme f(x)= 1/3 x^3+3/2 x^2-4x ?
The extreme f(x)= 1/3 x^3+3/2 x^2-4x is Maximum(-4, 56/3),Minimum(1,-13/6)