1. Find the line tangent to the graph of where .

Solution:

Recall that a line can be written in the form where m is the slope of the line and lie on the line. In this case, we're looking for a line that passes through the point and has the slope of f at the point x = 25.

So, .

Now let's find m. The slope of f at the point (25, 6) is f'(25).

So,

So

So the equation of the line will be:

,

, or finally

Can you do the second one?