Let . The exact value of is approximately 7.0711. Consider the point P(49,7) on the…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Let f(x)=x. The exact value of 50 is approximately 7.0711.
Consider the point P(49,7) on the graph of f.
(a) Write the equation of the line tangent to the graph of f at P.
(b) Use the line found in part (a) to estimate 50. Show all work leading to your estimate.
(c) Compute the absolute error and the percent error of your estimate, using the given exact value 7.0711. Express the percent error to three decimal places.
(d) Explain how decreasing the difference Δx between 49 and the number being approximated would be expected to affect the percent error. Support your answer with reasoning involving local linearity.