What is the extreme f(x)= 4/3 x^3+3x^2-28x-44 ?

The extreme f(x)= 4/3 x^3+3x^2-28x-44 is Maximum(-7/2 , 403/12),Minimum(2,-232/3)

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extreme f(x)= 4/3 x^3+3x^2-28x-44

extreme points

f (x) = \frac{4}{3} x^{3} + 3 x^{2} - 28 x - 44

Maximum (- \frac{7}{2}, \frac{403}{12}), Minimum (2, - \frac{232}{3})

Solution steps

f^{'} (x) = 4 x^{2} + 6 x - 28

Find intervals:

Increasing

: - \infty < x < - \frac{7}{2},

Decreasing

: - \frac{7}{2} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{7}{2}

into

\frac{4}{3} x^{3} + 3 x^{2} - 28 x - 44 : \frac{403}{12}

Maximum (- \frac{7}{2}, \frac{403}{12})

Plug

x = 2

into

\frac{4}{3} x^{3} + 3 x^{2} - 28 x - 44 : - \frac{232}{3}

Minimum (2, - \frac{232}{3})

Maximum (- \frac{7}{2}, \frac{403}{12}), Minimum (2, - \frac{232}{3})

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

f (x) = - x^{4} + 2 x^{3} + 8 x

f (x) = - x^{3}

f (x) = x^{2} + 10

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 6 x + 7 y

What is the extreme f(x)= 4/3 x^3+3x^2-28x-44 ?
The extreme f(x)= 4/3 x^3+3x^2-28x-44 is Maximum(-7/2 , 403/12),Minimum(2,-232/3)