1. 5.2: Linear Approximation

2. Today we are using that tangent line to approximate the value of the function.

3. Warm-Up Function f(x) has the properties f’(x)>0 and f’’(x)<0. If you used the equation of a tangent line to the function to approximate a value of f(x). The approximation would be…. I.Less than f(x) II.Same as f(x) III.Greater than f(x)

4. The function R(t) measures the number of people that have entered an auditorium, where R(t) is measured in hundreds of people and t is measured in hours. a) Find f’( ) and use the correct units b) Find the equation of a tangent line at t= c) Using the tangent line at t=, approximate the number of people in the auditorium at t=1.