What is the extreme f(x)= 2/3 x^3+11/2 x^2-21x+5 ?

The extreme f(x)= 2/3 x^3+11/2 x^2-21x+5 is Maximum(-7, 1157/6),Minimum(3/2 ,-95/8)

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extreme f(x)= 2/3 x^3+11/2 x^2-21x+5

extreme points

f (x) = \frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5

Maximum (- 7, \frac{1157}{6}), Minimum (\frac{3}{2}, - \frac{95}{8})

Solution steps

f^{'} (x) = 2 x^{2} + 11 x - 21

Find intervals:

Increasing

: - \infty < x < - 7,

Decreasing

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

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - 7

into

\frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5 : \frac{1157}{6}

Maximum (- 7, \frac{1157}{6})

Plug

x = \frac{3}{2}

into

\frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5 : - \frac{95}{8}

Minimum (\frac{3}{2}, - \frac{95}{8})

Maximum (- 7, \frac{1157}{6}), Minimum (\frac{3}{2}, - \frac{95}{8})

f (x) = (x - 3) e^{- 5 x}

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

g (x) = e^{- x^{4}}, - 3 \leq x \leq 1

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

f (x, y) = 2^{3} - y^{2} + 2 x y + 1

What is the extreme f(x)= 2/3 x^3+11/2 x^2-21x+5 ?
The extreme f(x)= 2/3 x^3+11/2 x^2-21x+5 is Maximum(-7, 1157/6),Minimum(3/2 ,-95/8)