What is the extreme f(x)=5x^2-30x,0<= x<= 5 ?

The extreme f(x)=5x^2-30x,0<= x<= 5 is Maximum(0,0),Minimum(3,-45),Maximum(5,-25)

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extreme f(x)=5x^2-30x,0<= x<= 5

extreme points

f (x) = 5 x^{2} - 30 x, 0 \leq x \leq 5

Maximum (0, 0), Minimum (3, - 45), Maximum (5, - 25)

Solution steps

Find the critical points:

x = 0, x = 3, x = 5

Domain of

5 x^{2} - 30 x, 0 \leq x \leq 5 : 0 \leq x \leq 5

Find intervals:

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < 5

Plug the extreme point

x = 0

into

5 x^{2} - 30 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 3

into

5 x^{2} - 30 x \Rightarrow y = - 45

Minimum (3, - 45)

Plug the extreme point

x = 5

into

5 x^{2} - 30 x \Rightarrow y = - 25

Maximum (5, - 25)

Maximum (0, 0), Minimum (3, - 45), Maximum (5, - 25)

x \cdot e^{- x^{2}}

\frac{2 x + 4}{x ^{2} + 4}

f (x, y) = (5 x^{2} + 7 y^{2}) e^{- y}

8 - 4 x

f (x) = x^{2} - x - 2, 0 \leq x \leq 2

What is the extreme f(x)=5x^2-30x,0<= x<= 5 ?
The extreme f(x)=5x^2-30x,0<= x<= 5 is Maximum(0,0),Minimum(3,-45),Maximum(5,-25)