What is the extreme f(x)= 2/3 x-5,-2<= x<= 3 ?

The extreme f(x)= 2/3 x-5,-2<= x<= 3 is Minimum(-2,-19/3),Maximum(3,-3)

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extreme f(x)= 2/3 x-5,-2<= x<= 3

extreme points

f (x) = \frac{2}{3} x - 5, - 2 \leq x \leq 3

Minimum (- 2, - \frac{19}{3}), Maximum (3, - 3)

Solution steps

Find the critical points:

x = - 2, x = 3

Domain of

\frac{2}{3} x - 5, - 2 \leq x \leq 3 : - 2 \leq x \leq 3

Find intervals:

Increasing

: - 2 < x < 3

Plug the extreme point

x = - 2

into

\frac{2}{3} x - 5 \Rightarrow y = - \frac{19}{3}

Minimum (- 2, - \frac{19}{3})

Plug the extreme point

x = 3

into

\frac{2}{3} x - 5 \Rightarrow y = - 3

Maximum (3, - 3)

Minimum (- 2, - \frac{19}{3}), Maximum (3, - 3)

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

f (x, y) = 12 - x^{2} - y^{2}

f (x, y) = x + y + x y

f (x) = 1 + \frac{5}{x} - \frac{8}{x ^{2}}

What is the extreme f(x)= 2/3 x-5,-2<= x<= 3 ?
The extreme f(x)= 2/3 x-5,-2<= x<= 3 is Minimum(-2,-19/3),Maximum(3,-3)