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Find the line tangent to

+2 votes

f(x)=2e^x at x=3?

asked Jan 31, 2013 in CALCULUS by anonymous Apprentice
reshown Jan 31, 2013 by bradely

1 Answer

+3 votes

f(x) = 2ex

Apply derivative each side.

f'(x) = 2ex

If x = 3 then f'(3) = 2e3

Here slope is 2e3

Now you need a point, we know it touches at x = 3, so we want (3, f(3)) = (3, 2e3)

The straight-line equations is called the "point-slope" form. For this one, they give you a point (x, y) and a slope m, and have you plug it into this formula: y - y₁ = m(x - x₁)

y - 2e3 = 2e3(x - 3)

y - 2e3 = 2xe3 - 6e3

Add 2e3 to each side.

y = 2xe3 - 4e3

The tangent line equation is y = 2xe3 - 4e3.

answered Jan 31, 2013 by richardson Scholar

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