What is the extreme f(x)=x+10sqrt(1-x),-2<= x<= 5 ?

The extreme f(x)=x+10sqrt(1-x),-2<= x<= 5 is Maximum(-2,-2+10sqrt(3)),Minimum(1,1)

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extreme f(x)=x+10sqrt(1-x),-2<= x<= 5

extreme points

f (x) = x + 10 1 - x, - 2 \leq x \leq 5

Maximum (- 2, - 2 + 103), Minimum (1, 1)

Solution steps

Find the critical points:

x = - 2, x = 1

Domain of

x + 10 1 - x, - 2 \leq x \leq 5 : - 2 \leq x \leq 1

Find intervals:

Decreasing

: - 2 < x < 1

Plug the extreme point

x = - 2

into

x + 10 1 - x \Rightarrow y = - 2 + 103

Maximum (- 2, - 2 + 103)

Plug the extreme point

x = 1

into

x + 10 1 - x \Rightarrow y = 1

Minimum (1, 1)

Maximum (- 2, - 2 + 103), Minimum (1, 1)

What is the extreme f(x)=x+10sqrt(1-x),-2<= x<= 5 ?
The extreme f(x)=x+10sqrt(1-x),-2<= x<= 5 is Maximum(-2,-2+10sqrt(3)),Minimum(1,1)