What is the tangent of f(x)=6e^{-0.6x},\at x=4 ?

The tangent of f(x)=6e^{-0.6x},\at x=4 is y=-0.32658…x+6/(e^{2.4)}+1.30633…

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tangent of f(x)=6e^{-0.6x},\at x=4

tangent of

f (x) = 6 e^{- 0.6 x}, at x = 4

y = - 0.32658 \dots x + \frac{6}{e ^{2.4}} + 1.30633 \dots

Solution steps

Find the tangent point:

(4, \frac{6}{e ^{2.4}})

Find the slope of

f (x) = 6 e^{- 0.6 x} : \frac{df ( x )}{d x} = - 3.6 e^{- 0.6 x}

Compute the slope of

f (x) = 6 e^{- 0.6 x}

x = 4 : m = - 0.32658 \dots

Find the line with slope m=

- 0.32658 \dots

and passing through

(4, \frac{6}{e ^{2.4}}) : y = - 0.32658 \dots x + \frac{6}{e ^{2.4}} + 1.30633 \dots

y = - 0.32658 \dots x + \frac{6}{e ^{2.4}} + 1.30633 \dots

\int (y - 1) d y

\int - 0.5 y d y

\frac{\partial}{\partial x} (x e^{4 x})

2 x = y, x + y = 4, x + y = 12

What is the tangent of f(x)=6e^{-0.6x},\at x=4 ?
The tangent of f(x)=6e^{-0.6x},\at x=4 is y=-0.32658…x+6/(e^{2.4)}+1.30633…