Question

What is the equation of the tangent line to the curve f(x) = sqrt(x+5) at the point (4,3) ?
Please use Limits...

Answer 1

\[\lim_{h \rightarrow 0}(\frac{ f(x+h)-f(x) }{ h })\]

Answer 2

That's the right formula to use to find the slope. Just apply the f(x) and solve. Since h is approaching zero, you should end up being able to eliminate h from the simplified equation and end up with an x term or an integer. You put the x part of your coordinate pair into this, and that is your slope. Then you just need to put that and the point into point-slope form and if your teacher prefers y=mx+b form, convert it into that with the necessary steps. I hope that helps!