What is the extreme f(x)= 1/3 x^3-7/2 x^2+6x+1 ?

The extreme f(x)= 1/3 x^3-7/2 x^2+6x+1 is Maximum(1, 23/6),Minimum(6,-17)

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extreme f(x)= 1/3 x^3-7/2 x^2+6x+1

extreme points

f (x) = \frac{1}{3} x^{3} - \frac{7}{2} x^{2} + 6 x + 1

Maximum (1, \frac{23}{6}), Minimum (6, - 17)

Solution steps

f^{'} (x) = x^{2} - 7 x + 6

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 1

into

\frac{1}{3} x^{3} - \frac{7}{2} x^{2} + 6 x + 1 : \frac{23}{6}

Maximum (1, \frac{23}{6})

Plug

x = 6

into

\frac{1}{3} x^{3} - \frac{7}{2} x^{2} + 6 x + 1 : - 17

Minimum (6, - 17)

Maximum (1, \frac{23}{6}), Minimum (6, - 17)

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

f (x) = \frac{2 x ^{2} + 5}{x ^{2} - 25}

f (x, y) = x - 5 y + 6

f (x) = 2 x - 6 x^{\frac{1}{3}}

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 11

What is the extreme f(x)= 1/3 x^3-7/2 x^2+6x+1 ?
The extreme f(x)= 1/3 x^3-7/2 x^2+6x+1 is Maximum(1, 23/6),Minimum(6,-17)