Find an equation of the tangent line to the given curve at the specified point.

Question

Find an equation of the tangent line to the given curve at the specified point.

y = 1 + x/ 8 + e^x

,

(0, 1/9)

Answer 1

Hi Oa D.,

So did you sketch your function, and locate the specified point? Since the point is NOT on the function curve -- the curve has two separate pieces governed by the x/8 term -- there will be I think just one tangent line possible, the one to a point with positive x value, somewhere substantially to the right of the origin. The other three potential "tangent" lines can't be solved, because the limiting slopes are ->0- and ->.negativeinfinity. for x<0, and ->.negativeinfinity. for x->0+. (Asymptotes aren't tangents!) So draw it, solve for the slope (you have one "arbitrary" point ON the function curve, and the given point), and also you can form the first derivative of the function which mu.st equal that slope at the "arbitrary" point (for a tangent line!).

Even if you can't solve that equation exactly, you can do it numerically to approximate.

-- Did you attempt the above?

--Cheers, --Mr. d.