What is the tangent of f(x)=20(x-1)e^{-0.5x},\at x=4 ?

The tangent of f(x)=20(x-1)e^{-0.5x},\at x=4 is y=-1.35335…x+(60)/(e^2)+5.41341…

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tangent of f(x)=20(x-1)e^{-0.5x},\at x=4

tangent of

f (x) = 20 (x - 1) e^{- 0.5 x}, at x = 4

y = - 1.35335 \dots x + \frac{60}{e ^{2}} + 5.41341 \dots

Solution steps

Find the tangent point:

(4, \frac{60}{e ^{2}})

Find the slope of

f (x) = 20 (x - 1) e^{- 0.5 x} : \frac{df ( x )}{d x} = 20 (- 0.5 e^{- 0.5 x} x + 1.5 e^{- 0.5 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 = - 1.35335 \dots

Find the line with slope m=

- 1.35335 \dots

and passing through

(4, \frac{60}{e ^{2}}) : y = - 1.35335 \dots x + \frac{60}{e ^{2}} + 5.41341 \dots

y = - 1.35335 \dots x + \frac{60}{e ^{2}} + 5.41341 \dots

What is the tangent of f(x)=20(x-1)e^{-0.5x},\at x=4 ?
The tangent of f(x)=20(x-1)e^{-0.5x},\at x=4 is y=-1.35335…x+(60)/(e^2)+5.41341…