What is the tangent of f(x)=e^x,\at x=5 ?

The tangent of f(x)=e^x,\at x=5 is y=e^5x-4e^5

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tangent of f(x)=e^x,\at x=5

tangent of

f (x) = e^{x}, at x = 5

y = e^{5} x - 4 e^{5}

Solution steps

Find the tangent point:

(5, e^{5})

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^{5}

Find the line with slope m=

e^{5}

and passing through

(5, e^{5}) : y = e^{5} x - 4 e^{5}

y = e^{5} x - 4 e^{5}

What is the tangent of f(x)=e^x,\at x=5 ?
The tangent of f(x)=e^x,\at x=5 is y=e^5x-4e^5