MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the function g(x)=sinx. Approximate g′(1.2) using tabulated values of g shown below.
x
1.10
1.19
1.20
1.21
1.30
g(x)
0.891207
0.928960
0.932039
0.934986
0.963558
Answer each part carefully and show all supporting work.
(a) Using the points x=1.10 and x=1.30, compute an estimate of g′(1.2). Clearly label your units.
(b) Using the points x=1.19 and x=1.21, compute a second estimate of g′(1.2).
(c) The exact derivative satisfies g′(x)=cosx. Evaluate g′(1.2) exactly and determine the percent error for each estimate found in parts (a) and (b).
(d) Identify which estimate is more accurate and explain, in quantitative terms, why its error is smaller.