Expert: Paul Klarreich - 10/14/2009

Question
f(x)=x^2+3e^x, at Q(1,1+3e)

Answer
Questioner: jen
Country: Canada
Category: Calculus
Private: No
Subject: Find the equation of the tangent line through the given point
Question: f(x)=x^2+3e^x, at Q(1,1+3e)
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Hi, Jen,

You are almost there.  If your T.L. passes through Q(1,1+3e), and the equation of any line has the form:

y - y0 = m(x - x0)

then all you need is the slope, m, at  x = 1.  For that, find the derivative:

f'(x) = 2x + 3e^x

f'(1) = 2 + 3e = m

So write:

y - (1 + 3e) = (2 + 3e)(x - 1)

Simplify that a bit and you are home.