Transcript
1) The demand function at a price P is given by f(p)=3000-2p. Is the elasticity of demand at a price of $ 900 elastic, inelastic, or unitary?
Ep=pq?dqdp=p3000-2p?-2
At p=900 we get
E900=9001200?-2=-32<-1
At a price p=$900 the elasticity of demand is elastic.
2) A company manufactures and sells X clocks per week with weekly
price-demand function: f(p)=20-2p where p is the price per clock.
a) Compute the elasticity of demand function, E(p), for this demand
function.
Ep=pq?dqdp=p20-2p?-2=pp-10
b) At P=2, a price increase of 10% will create a demand decrease of
what percent?
qold=20-2pold=20-4=16
qnew=20-2pnew=20-4.4=15.6
qnew-qoldqold=-0.416=-0.025=-2.5%
2.5 % decrease
3) Suppose that the demand for a certain item is
q=10+1p2
Evaluate the elasticity of demand at the point where the price is 0.5.
Ep=pq?dqdp=p10+p-2?-1p3=-110p2+1
E0.5=-110×0.25+1=-13.5=-27?-0.2857
E(0.5)=-2/7=-0.2857
4) The price-demand equation is given by q+p=6000.
a) Write demand as a function of price.
f(p)=6000-p
b)Find the elasticity of demand at a price of $ 20000.
Ep=pq?dqdp=p6000-p?-1=pp-6000
E2000=-20004000=-12
c) If the price increases 10 % from a price of $ 20000,
what is the approximate (percentage) decrease in demand?
qold=6000-pold=6000-2000=4000
qnew=6000-pnew=6000-2200=3800
qnew-qoldqold=-2004000=-0.20=-20%
Answer: 20 % decrease
The function h(X) has the following graph
Find the value of X that gives the absolute maximum and the absolute
minimum of h(x) over the given interval
[-5,5]
absolute maximum at X = -2
absolute minimum at X = +2
[-1,1]
absolute maximum at X = -1
absolute minimum at X = +1
[0,3]
absolute maximum at X = 0
absolute minimum at X = +2
2) Consider the function . f(x)=3-2x2, -5 <=X <= 1
The absolute maximum value is 3 and this occurs at X equals 0
The absolute minimum value is -47 and this occurs at X equals -5
3) Consider the function. f(x)=6x2-6x+1, 0<=X<=7
The absolute maximum of f(x)(on the given interval) is 259
and the absolute minimum of f(x)(on the given interval) is -1/2
4) The function f(x)=2x3-33x2+144x+7 has one
local minimum and one local maximum.
This function has a local minimum at x =8 with value 71 and a local maximum at x=3 with value 196.
5) Consider the function .
f(x)=2x3+6x2-90x+6, -5<=x<=4
This function has an absolute minimum value equal to -156 reached when x=3
and an absolute maximum value equal to 356 reached when x=-5.
6) Consider the function .
f(x)=-5x2+8x-10. f(x)is increasing on the interval (-infinity, A]
and decreasing on the interval [A, infinity) where A is the
critical number.
Find A. A=4/5 =0.8
At x=A, does f(x) have a local min, a local max, or neither?
Type in your answer as LMIN, LMAX, or NEITHER.
At x=0.8 the function has a local max (LMAX).
7) Let f(x)=x3-23x. On each interval below, find the value of x
where the absolute maximum and the absolute minimum of f(x) occur,
if they exist. If the absolute maximum or minimum does not exist,
write "DNE".
(a) (-infinity, infinity)
absolute max at x =DNE
absolute min at x = DNE
(b) [-4, infinity)
absolute max at x = DNE
absolute min at x = ?693
(c) [-4, 0]
absolute max at x = -?693
absolute min at x = 0
(d) [0, 10]
absolute max at x = 10
absolute min at x =?693
