What is the extreme f(x)= 2/3 x^3+1/2 x^2-21x+2 ?

The extreme f(x)= 2/3 x^3+1/2 x^2-21x+2 is Maximum(-7/2 , 1273/24),Minimum(3,-77/2)

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extreme f(x)= 2/3 x^3+1/2 x^2-21x+2

extreme

Maximum (- \frac{7}{2}, \frac{1273}{24}), Minimum (3, - \frac{77}{2})

Solution steps

f^{'} (x) = 2 x^{2} + x - 21

Find intervals:

Increasing

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

Decreasing

: - \frac{7}{2} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - \frac{7}{2}

into

\frac{2}{3} x^{3} + \frac{1}{2} x^{2} - 21 x + 2 : \frac{1273}{24}

Maximum (- \frac{7}{2}, \frac{1273}{24})

Plug

x = 3

into

\frac{2}{3} x^{3} + \frac{1}{2} x^{2} - 21 x + 2 : - \frac{77}{2}

Minimum (3, - \frac{77}{2})

Maximum (- \frac{7}{2}, \frac{1273}{24}), Minimum (3, - \frac{77}{2})

What is the extreme f(x)= 2/3 x^3+1/2 x^2-21x+2 ?
The extreme f(x)= 2/3 x^3+1/2 x^2-21x+2 is Maximum(-7/2 , 1273/24),Minimum(3,-77/2)