What is the tangent of f(x)=e^{x^2},\at x= 1/2 ?

The tangent of f(x)=e^{x^2},\at x= 1/2 is y=e^{1/4}x+(e^{1/4})/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)=e^{x^2},\at x= 1/2

tangent of

f (x) = e^{x^{2}}, at x = \frac{1}{2}

y = e^{\frac{1}{4}} x + \frac{e ^{\frac{1}{4}}}{2}

Solution steps

Find the tangent point:

(\frac{1}{2}, e^{\frac{1}{4}})

Find the slope of

f (x) = e^{x^{2}} : \frac{df ( x )}{d x} = e^{x^{2}} \cdot 2 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = e^{\frac{1}{4}}

Find the line with slope m=

e^{\frac{1}{4}}

and passing through

(\frac{1}{2}, e^{\frac{1}{4}}) : y = e^{\frac{1}{4}} x + \frac{e ^{\frac{1}{4}}}{2}

y = e^{\frac{1}{4}} x + \frac{e ^{\frac{1}{4}}}{2}

What is the tangent of f(x)=e^{x^2},\at x= 1/2 ?
The tangent of f(x)=e^{x^2},\at x= 1/2 is y=e^{1/4}x+(e^{1/4})/2