MATH 142 Business Math II, Week In Review
Spring, 2015, Problem Set 5 (4.4, 4.5, 5.1)
JoungDong Kim
1. Find the derivative of function.
(a) f (x) = e−0.1x
(b) f (x) = e4x
(c) f (x) = e
(d) f (x) =
3 −x−1
√
3x
√
3
xex
(e) f (x) = (x3 − 2)e2x
1
(f) f (x) =
ex
x2 + 1
(g) f (x) =
√
x3 e3x
(h) f (x) =
√
2 + e−3x
(i) f (x) = 33x
(j) f (x) = 7x
7
(k) f (x) = 3x · 5x
(l) f (x) = ln(x4 + x2 + 3)
2
(m) f (x) =
ln(x2 )
x+1
(n) f (x) =
ln(x2 )
ex + e−x
(o) f (x) =
√
ln x,
2
(p) f (x) = ex · ln x,
(q) f (x) = ln(x7 ),
(x > 0)
(x > 0)
(x > 0)
3
2
2. Suppose the profit equation is given by p(x) = x · e−0.5x . Find the marginal profit, and find where
the marginal profit is zero.
3. Find f ′ (x).
(a) f (x) = ee
ex
(b) f (x) = ln[ln(ln x)]
4
4. According to Stone and Rowe, the price elasticity of furniture is 3.04. If the price of furniture is
increased by 10%, what will happen to the demand for furniture?
5. A restaurant owner sells 100 dinner specials for $10 each. After raising the price to $11, she
noticed that only 70 specials were sold. What is the elasticity of demand?
5
6. Find the elasticity E at the given points and determine whether demand is inelastic, elastic, or
unit elastic.
(a) x = 20 − 4p,
1
(b) x = 10 + ,
p
10
(c) x = √ ,
p
p = 1,
p = 2.5, and p = 4
p = 0.1 and p = 1
p = 1 and p = 3
6
7. Find all critical values, the largest open intervals on which f is increasing, the largest open intervals
on which f is decreasing, and all relative maxima and minima.
(a) f (x) = −2x2 + 8x − 1
(b) f (x) = −4x6 − 6x4 + 5
7
(c) f (x) = 1 − ln x
(d) f (x) = e−x
2
8
8. If the demand equation for a function is given by p = −0.2x + 16, find the value of x for which
revenue is maximum.
9