Find an equation for the tangent line to the graph of the function h(x)=(5x+11)/(sqrt(x^2+5) at the point (2,7).

Question

Hello, the examples on the book are different than this question and I am confused. The answer is (1/9)x + (61/9) but I do not know how to get there and need the work to do so. Thank you!

Answer 1

I am not going to do this problem for you because the derivative you need to calculate is a mess. I will tell you how to do it.

First you need to compute h'(x) and evaluate it at x=2

Remember how to do the derivative of a fraction: my students taught me this one

----> downsie d upsie - upside d downsie divided by downsie squared

Then set the value of the derivative at x=2 to (y-7)/(x-2).and that is your answer.