What is the extreme f(x)= 1/3 x^3-5x^2+21x-16 ?

The extreme f(x)= 1/3 x^3-5x^2+21x-16 is Maximum(3,11),Minimum(7, 1/3)

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extreme f(x)= 1/3 x^3-5x^2+21x-16

extreme points

f (x) = \frac{1}{3} x^{3} - 5 x^{2} + 21 x - 16

Maximum (3, 11), Minimum (7, \frac{1}{3})

Solution steps

f^{'} (x) = x^{2} - 10 x + 21

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = 3

into

\frac{1}{3} x^{3} - 5 x^{2} + 21 x - 16 : 11

Maximum (3, 11)

Plug

x = 7

into

\frac{1}{3} x^{3} - 5 x^{2} + 21 x - 16 : \frac{1}{3}

Minimum (7, \frac{1}{3})

Maximum (3, 11), Minimum (7, \frac{1}{3})

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

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

f (x, y) = x^{3} + y^{2} - 6 x^{2} + y - 1

f (x) = x^{2} - 5 x + 1

f (x, y) = e^{4 x y} + 5 y

What is the extreme f(x)= 1/3 x^3-5x^2+21x-16 ?
The extreme f(x)= 1/3 x^3-5x^2+21x-16 is Maximum(3,11),Minimum(7, 1/3)