# Equations of Tangent Lines

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What is the equation of the tangent line to f(x) = bar e^(x^2) at x = 2?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Answer: D

Since f(x)=e^(x^2), then f'(x)=2xe^(x^2)

At the point x=2, we have

f(2)=e^4 and f'(2)=4e^4

Then the tangent line is

y-f(2)=f'(2)(x-2), then

y-e^4=4e^4(x-2)=4e^4 x - 8e^4

Then we get

y=4e^4 x - 7e^4.

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