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AP Calculus AB. Day 13 Section 3.9. 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.

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ap calculus ab

AP Calculus AB

Day 13

Section 3.9

Perkins

linear approximation
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.

slide4
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.

ap calculus ab1

AP Calculus AB

Day 13

Section 3.9

Perkins

slide9
Finding Differentials

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

Change in y.

Change in x.

Slope of tangent line at a given x.

3. Estimate f(0.03) without your calculator.

4. Estimate f(8.96) without your calculator.

slide10
Finding Differentials

3. Estimate f(0.03) without your calculator.

4. Estimate f(8.96) without your calculator.

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