What is the tangent of f(x)=ln(x),\at x=e^{-7} ?

The tangent of f(x)=ln(x),\at x=e^{-7} is y=e^7x-8

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tangent of f(x)=ln(x),\at x=e^{-7}

tangent of

f (x) = ln (x), at x = e^{- 7}

y = e^{7} x - 8

Solution steps

Find the tangent point:

(e^{- 7}, - 7)

Find the slope of

f (x) = ln (x) : \frac{df ( x )}{d x} = \frac{1}{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^{7}

Find the line with slope m=

e^{7}

and passing through

(e^{- 7}, - 7) : y = e^{7} x - 8

y = e^{7} x - 8

What is the tangent of f(x)=ln(x),\at x=e^{-7} ?
The tangent of f(x)=ln(x),\at x=e^{-7} is y=e^7x-8