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Popular >

extreme y=x^7e^x+4

Solution

extreme points

y = x^{7} e^{x} + 4

Solution

Minimum (- 7, - \frac{823543}{e ^{7}} + 4), Saddle (0, 4)

Solution steps

f^{'} (x) = e^{x} x^{7} + 7 e^{x} x^{6}

Find intervals:

Decreasing

: - \infty < x < - 7,

Increasing

: - 7 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 7

into

x^{7} e^{x} + 4 : - \frac{823543}{e ^{7}} + 4

Minimum (- 7, - \frac{823543}{e ^{7}} + 4)

Plug

x = 0

into

x^{7} e^{x} + 4 : 4

Saddle (0, 4)

Minimum (- 7, - \frac{823543}{e ^{7}} + 4), Saddle (0, 4)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme y=x^7e^x+4 ?
The extreme y=x^7e^x+4 is Minimum(-7,-(823543)/(e^7)+4),Saddle(0,4)