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

The tangent of f(x)=e^x,\at x=2 is y=e^2x-e^2

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tangent of f(x)=e^x,\at x=2

tangent of

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

y = e^{2} x - e^{2}

Solution steps

Find the tangent point:

(2, e^{2})

Find the slope of

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

Find the line with slope m=

e^{2}

and passing through

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

y = e^{2} x - e^{2}

What is the tangent of f(x)=e^x,\at x=2 ?
The tangent of f(x)=e^x,\at x=2 is y=e^2x-e^2