What is the tangent of f(x)=3-e^{-3x},\at x=-ln(2) ?

The tangent of f(x)=3-e^{-3x},\at x=-ln(2) is y=24x-5+24ln(2)

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tangent of f(x)=3-e^{-3x},\at x=-ln(2)

tangent of

f (x) = 3 - e^{- 3 x}, at x = - ln (2)

y = 24 x - 5 + 24 ln (2)

Solution steps

Find the tangent point:

(- ln (2), - 5)

Find the slope of

f (x) = 3 - e^{- 3 x} : \frac{df ( x )}{d x} = 3 e^{- 3 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 = 24

Find the line with slope m=

24

and passing through

(- ln (2), - 5) : y = 24 x - 5 + 24 ln (2)

y = 24 x - 5 + 24 ln (2)

What is the tangent of f(x)=3-e^{-3x},\at x=-ln(2) ?
The tangent of f(x)=3-e^{-3x},\at x=-ln(2) is y=24x-5+24ln(2)