What is the tangent of f(x)=e^x ?

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

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tangent of f(x)=e^x

tangent of

f (x) = e^{x}

y = e^{a_{0}} x + e^{a_{0}} - e^{a_{0}} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{a_{0}})

Find the slope of

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

Compute the slope of

f (x) = e^{x}

x = a_{0} : m = e^{a_{0}}

Find the line with slope m=

e^{a_{0}}

and passing through

(a_{0}, e^{a_{0}}) : y = e^{a_{0}} x + e^{a_{0}} - e^{a_{0}} a_{0}

y = e^{a_{0}} x + e^{a_{0}} - e^{a_{0}} a_{0}

f (x) = x, at x = 1

y = 2^{x}

x = 1

(3, 3)

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

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