en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=e^x-2x

Solution

extreme points

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

Solution

Minimum (ln (2), 2 - 2 ln (2))

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < ln (2),

Increasing

: ln (2) < x < \infty

Plug

x = ln (2)

into

e^{x} - 2 x : 2 - 2 ln (2)

Minimum (ln (2), 2 - 2 ln (2))

Graph

Popular Examples

extreme f(x,y)=ln(x^2+4y^2-4)extreme points

f (x, y) = ln (x^{2} + 4 y^{2} - 4)

extreme f(x)=cos^2(x),0<= x<= pi extreme points

f (x) = cos^{2} (x), 0 \leq x \leq π

extreme f(x)=x^3+2x^2-7x extreme points

f (x) = x^{3} + 2 x^{2} - 7 x

extreme f(x,y)=xe^{-3x^2-3y^2}extreme points

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

extreme f(x,y)=2x^2-8x+y^2-8y+2 extreme points

f (x, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 2

Frequently Asked Questions (FAQ)

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