(a)
(b)
(b)
(c)
Find the dimensions of the smallest rectangle that contains R and
has sides parallel to the x- and y-axes.
Find the area of R.
(a) For what positive values of x does converge?
How many terms are needed to estimate f(0.5) to within 0.01?
Would an estimate for f(−0.5) using the same number of terms be
more accurate, less accurate, or the same? Explain.
Part B. Directions: Answer these questions without using your calculator.
Draw a graph of y = f(x), given that f satisfies all the following
conditions:
(1) f ′(−1) = f ′(1) = 0.
(2) If x < −1, f ′(x) > 0 but f ′′ < 0.
(3) If −1 < x < 0, f ′(x) > 0 and f ′′ > 0.
(4) If 0 < x < 1, f ′(x) > 0 but f ′′ < 0.
(5) If x > 1, f ′(x) < 0 and f ′′ < 0.
The figure below shows the graph of f ′, the derivative of f, with domain
−3 ≤ x ≤ 9. The graph of f ′ has horizontal tangents at x = 2 and x = 4, and
a corner at x = 6.
