What is the tangent of f(x)=e^{x/3} ?

The tangent of f(x)=e^{x/3} is y=e^{(a_{0})/3} 1/3 x+e^{(a_{0})/3}-e^{(a_{0})/3} 1/3 a_{0}

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tangent of f(x)=e^{x/3}

tangent of

f (x) = e^{\frac{x}{3}}

y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{\frac{a _{0}}{3}})

Find the slope of

f (x) = e^{\frac{x}{3}} : \frac{df ( x )}{d x} = e^{\frac{x}{3}} \frac{1}{3}

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{a _{0}}{3}} \frac{1}{3}

Find the line with slope m=

e^{\frac{a _{0}}{3}} \frac{1}{3}

and passing through

(a_{0}, e^{\frac{a _{0}}{3}}) : y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

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\int_{\frac{9}{2}}^{9} 81 - x^{2} d x

What is the tangent of f(x)=e^{x/3} ?
The tangent of f(x)=e^{x/3} is y=e^{(a_{0})/3} 1/3 x+e^{(a_{0})/3}-e^{(a_{0})/3} 1/3 a_{0}