The linear approximation

Question

The linear approximation at  to  is  where  is:     and where  is:

Answer 1

Hello Lola,

I will write out the steps you need to do. See if you can fill in the missing details and get the answer.

The answer to this problem will be a line equation. Think of y = mx + b. We need slope m and y-intercept b.

As you know, in calculus, we have a fancy name for the slope which is "derivative".

Since y = sin(4x). Find y ' and substitute x = 0 to get the slope which is the m.

Think of the graph of y = sin(4x) at x = 0. It will have y = 0 which makes the point (0, 0).

So the linear approximation (which is the same as the tangent line) will go through (0, 0). This means the

y-intercept is (0, 0) so b = 0. This means y = mx + 0 or y = mx.

Use the m from your derivative answer and make the correct equation.