Determining the equation for the line that's tangent to a graph.

Question

Hello,

I have this question that I'm struggling with:

Find an equation of the line that is tangent to the graph of:

f (x) = 4 / sqrt(2-x) at the point (1,4). Use the tangent line to approximate f(1.01).

I think I'd first have to multiply the right side of the equation by sqrt(2-x) / sqrt(2-x). Am I on the right path so far?

Answer 1

You find the derivative of the function. From this, you can get the slope of the tangent line at (1,4).

Then, from the slope and knowing that the point (1, 4) is on this line, you can determine y = mx + b. Then, substitute 1.01 for x.

An alternative: you can just start from the point (1, 4) and say f(1.1) = f(1) + f'(1)(1.1- 1) or 4 + .1 f'(1)