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Popular >

extreme f(x)=(x-3)e^x+3

Solution

extreme points

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

Solution

Minimum (2, - e^{2} + 3)

Solution steps

f^{'} (x) = e^{x} (x - 2)

Find intervals:

Decreasing

: - \infty < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 2

into

(x - 3) e^{x} + 3 : - e^{2} + 3

Minimum (2, - e^{2} + 3)

Graph

Popular Examples

extreme x^4+x^2 extreme points

x^{4} + x^{2}

extreme f(x)=x^7-4x^5+10 extreme points

f (x) = x^{7} - 4 x^{5} + 10

extreme f(x)=sqrt(x^2+16)extreme points

f (x) = x^{2} + 16

extreme f(x)=x^2-6x-9 extreme points

f (x) = x^{2} - 6 x - 9

extreme f(x)=2x^3+18x^2-42x+7,-7<= x<= 2 extreme points

f (x) = 2 x^{3} + 18 x^{2} - 42 x + 7, - 7 \leq x \leq 2

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x-3)e^x+3 ?
The extreme f(x)=(x-3)e^x+3 is Minimum(2,-e^2+3)