What is the tangent of y=3e^x,\at x=2 ?

The tangent of y=3e^x,\at x=2 is y=3e^2x-3e^2

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tangent of y=3e^x,\at x=2

tangent of

y = 3 e^{x}, at x = 2

y = 3 e^{2} x - 3 e^{2}

Solution steps

Find the tangent point:

(2, 3 e^{2})

Find the slope of

y = 3 e^{x} : \frac{d y}{d x} = 3 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 = 3 e^{2}

Find the line with slope m=

3 e^{2}

and passing through

(2, 3 e^{2}) : y = 3 e^{2} x - 3 e^{2}

y = 3 e^{2} x - 3 e^{2}

What is the tangent of y=3e^x,\at x=2 ?
The tangent of y=3e^x,\at x=2 is y=3e^2x-3e^2