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

The extreme f(x)=e^x(x-2),0<= x<= 2 is Maximum(0,-2),Minimum(1,-e),Maximum(2,0)

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

extreme points

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

Maximum (0, - 2), Minimum (1, - e), Maximum (2, 0)

Solution steps

Find the critical points:

x = 0, x = 1, x = 2

Domain of

e^{x} (x - 2), 0 \leq x \leq 2 : 0 \leq x \leq 2

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 2

Plug the extreme point

x = 0

into

e^{x} (x - 2) \Rightarrow y = - 2

Maximum (0, - 2)

Plug the extreme point

x = 1

into

e^{x} (x - 2) \Rightarrow y = - e

Minimum (1, - e)

Plug the extreme point

x = 2

into

e^{x} (x - 2) \Rightarrow y = 0

Maximum (2, 0)

Maximum (0, - 2), Minimum (1, - e), Maximum (2, 0)

(x + 11)^{2} - 14

f (t) = 3 + 2 ln (t)

x^{2} + 8

f (x) = \frac{3}{x ^{2} + 2 x}

f (x) = 3 x + 7

What is the extreme f(x)=e^x(x-2),0<= x<= 2 ?
The extreme f(x)=e^x(x-2),0<= x<= 2 is Maximum(0,-2),Minimum(1,-e),Maximum(2,0)