What is the extreme f(x)=(x+1)^7-7x-2 ?

The extreme f(x)=(x+1)^7-7x-2 is Maximum(-2,11),Minimum(0,-1)

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extreme f(x)=(x+1)^7-7x-2

extreme points

f (x) = (x + 1)^{7} - 7 x - 2

Maximum (- 2, 11), Minimum (0, - 1)

Solution steps

Find the critical points:

x = - 2, x = 0

Domain of

(x + 1)^{7} - 7 x - 2 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = - 2

into

(x + 1)^{7} - 7 x - 2 \Rightarrow y = 11

Maximum (- 2, 11)

Plug the extreme point

x = 0

into

(x + 1)^{7} - 7 x - 2 \Rightarrow y = - 1

Minimum (0, - 1)

Maximum (- 2, 11), Minimum (0, - 1)

f (x) = 7 x e^{- x}

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

375 x^{2} - 2250 x^{3}

f (x) = - 3 x^{4} + 12 x^{3} + 24 x^{2} + y^{2} - 49

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

What is the extreme f(x)=(x+1)^7-7x-2 ?
The extreme f(x)=(x+1)^7-7x-2 is Maximum(-2,11),Minimum(0,-1)