What is the extreme f(x)=(x^3)/3-(7x^2)/2+10x-4 ?

The extreme f(x)=(x^3)/3-(7x^2)/2+10x-4 is Maximum(2, 14/3),Minimum(5,-275/6+46)

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extreme f(x)=(x^3)/3-(7x^2)/2+10x-4

extreme points

f (x) = \frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 10 x - 4

Maximum (2, \frac{14}{3}), Minimum (5, - \frac{275}{6} + 46)

Solution steps

f^{'} (x) = x^{2} - 7 x + 10

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 2

into

\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 10 x - 4 : \frac{14}{3}

Maximum (2, \frac{14}{3})

Plug

x = 5

into

\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 10 x - 4 : - \frac{275}{6} + 46

Minimum (5, - \frac{275}{6} + 46)

Maximum (2, \frac{14}{3}), Minimum (5, - \frac{275}{6} + 46)

f (x) = \frac{4 x ^{2}}{x ^{2} - 4}

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

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

f (x) = x^{2} + 4 x

f (x, y) = 25 \cdot (y + x^{2})^{2} + (1 + x)^{2}

What is the extreme f(x)=(x^3)/3-(7x^2)/2+10x-4 ?
The extreme f(x)=(x^3)/3-(7x^2)/2+10x-4 is Maximum(2, 14/3),Minimum(5,-275/6+46)