MATH 171, PRACTICE TEST 3
Q1. Find the antiderivatives of
√
x x,
x3 + 1
√
x
Q2. Find the area under y = x2 from x = 1 to x = 3 using Riemann sums.
Q3. Find the critical numbers for f (x) = 2x3 − 9x2 + 12x + 2 and classify
them as local max or min.
Q4. Find the maximum and minimum values of
f (x) =
x−1
x2
on [1, 3].
Q5. Find the critical point of ex cos x in [0, π/2] and decide whether it is a
local max or min.
Q6. Find the minimum value of f (x) = 2x3/2 − 3x on [0, ∞).
Q7. Find the area under one arch of y = sin x.
Q8. A circular can with top is to be made with a fixed surface area S. Find
the dimensions that give the maximum volume.
Q9. Find the antiderivative of
1
x2 + 2x
+ ex +
.
3
x
1 + x2
Q10. A ball is dropped from the top of a cliff and hits the ground 2 seconds
later. How high was the cliff?