Let f (x) = 4x2 + 3.
(a) Find the tangent line to f at x = 3.
If f (1) = 2 and f ' (1) = 3, estimate f (1.2).
The picture below shows the tangent line to the function f at x = 0. Estimate f (-0.1).
The picture below shows a tangent line to f at x = a. What is f '(a)?
Let f (x) = cos2 x. Use a tangent line approximation to estimate f (0.1).
Let f (x) = x5 + 3x4 - 2x2 - x. Use a tangent line approximation to estimate f (.9).
Can a tangent line approximation ever produce the exact value of the function? Why or why not?
The function y = f (x) is a solution to the IVP
Approximate f (1.01).