1.(a)
(b)(c)
(d)2.(a)(b)
(c)3.(a)12 Miscellaneous Free-Response
Practice Exercises
These problems provide further practice for both parts of Section II of the
examination. Solutions to follow.
Part A. Directions: A graphing calculator is required for some of these problems. See instructions.A function f is continuous, differentiable, and strictly decreasing on the
interval [2.5,5]; some values of f are shown in the table above.
Estimate f ′(4.0) and f ′(4.8).
What does the table suggest may be true of the concavity of f ?
Explain.
Estimate with a Riemann Sum using left endpoints.
Set up (but do not evaluate) a Riemann Sum that estimates the
volume of the solid formed when f is rotated around the x-axis.The equation of the tangent line to the curve x^2 y − x = y 3 − 8 at the point
(0,2) is 12y + x = 24.
Given that the point (0.3,y 0 ) is on the curve, find y 0 approximately,
using the tangent line.
Find the true value of y 0.
What can you conclude about the curve near x = 0 from your
answers to parts (a) and (b)?
A differentiable function f defined on −7 < x < 7 has f(0) = 0 and f ′(x) =
2 x sin x − e−x^2 + 1. (Note: The following questions refer to f, not to f ′.)
Describe the symmetry of f.