Secant and Tangent Slope for f(x), given f(3 + h) − f(3) = e^2h − 1

[MasonAngus]

Suppose that f(x) is a function such that f(3 + h) − f(3) = e^2h − 1 for all h doesnt equal 0.
Find the slope of the secant line passing through the points (3, f(3)) and (5, f(5)).b)
Find the slope of the tangent line to the graph of f at x = 3.
I can get the tangent and secant slope if I have f(x) but because I don't I'm confused how to solve this. Can any one help? Thanks!

 

[MarkFL]

Let's start with part a.) We are given:

\(\displaystyle \Delta f=f(3+h)-f(3)=e^{2h}-1\)

\(\displaystyle \Delta x=h\)

Now, we can find \(\displaystyle h\) in this instance from:

\(\displaystyle 3+h=5\implies h=2\)

So, what is the slope \(\displaystyle m\) of the secant line?

\(\displaystyle \displaystyle m=\frac{\Delta f}{\Delta x}=\,?\)