1. 10/11/2014 Perkins AP Calculus AB Day 13 Section 3.9

2. Linear Approximation Non-calculator application of the tangent line. Used to estimate values of f(x) at ‘difficult’ x-values. (ex: 1.03, 2.99, 7.01) Steps: a.Find the equation of the tangent line to f(x) at an ‘easy’ value nearby. b.Plug the ‘difficult’ x-value in to get a reasonable estimate of what the actual y-value will be.

3. 1. Find the equation of the tangent line to f(x) at x = 1.

4. 2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01). This estimate will be accurate as long as the x-value is very close to the point of tangency.

5. 10/11/2014 Perkins AP Calculus AB Day 13 Section 3.9

6. Linear Approximation

7. 1. Find the equation of the tangent line to f(x) at x = 1.

8. 2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01).

9. Finding Differentials Change in y. Change in x. Slope of tangent line at a given x. 3. Estimate f(0.03) without your calculator. To estimate a y-value using a differential: 1. Find a y-value at a nearby x-value. 2. Add the value of your differential. Differential 4. Estimate f(8.96) without your calculator.

10. Finding Differentials 3. Estimate f(0.03) without your calculator. 4. Estimate f(8.96) without your calculator.