Question

Let f(x)=6x+16x^2 . Then the equation of the tangent line to the graph of f(x) at the point (2,16) is given by y=mx+b for

m= and b=

Answer 1

y = 16x^2 + 6x

y' = 32x + 6 for any x

The only problem I see is that y(2) = 76, so the point (2,16) is not on the graph.

So, now we have a line through (2,76) with slope y'(2) = 70

y-76 = 70(x-2) = 70x - 140
y = 70x - 64

Fix things up, and redo the steps above