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Math final exam

Terms in this set (27)

Find the equation of the tangent line to the graph of the given function at x=1
f(x)=2x³+3x
y=9x-4
find all values of x where the tangent line to the graph of the given equation is horizontal
y=4x²+16x+13
x=2
Evaluate the derivative f(x)=5x⁴-7x+4√x-8
20x³-7+(2/(x^½))
The annual net income of general electric for the period 2005-2009 is -2.25t²+10.6t+16
a) derivative of P
b) p(2)
c) Pderivative(2)
a) -4.5t+10.6
b) 28.2 billion dollars
c) 1.6 billion dollars per year
monthly profit of selling magazines is p(x)=4x+√x
a) find you're profit after you sell 50 magazines, round to 2 decimal places
b)find the marginal profit
a)207.07
b)4.07
The total sales of a company manufacturing bags is given by s(t)= 200t/(5+.03t) where t is the number of years since the start of 2000. at what rate were the sales changing at the start of 2004
26 bags per year
the society will charge students 1.20 per serving of pasta. the society estimates that the total cost of producing x servings of pasta at the event will be C(X)=120+.10x+.002x²

a)calculate the profit, P(x)
b)calculate the marginal profit, Pderivative(x)
c) compute the profit, p(200)
d) compute the marginal profit, p(200)
a) 1.10x-120-0.002x²
b)1.10-.004x
c)20
d).3
find the derivative of the function
g(x)=(3x⁴-5x³+6x²-4x+9)⁸
8(3x⁴-5x³+6x²-4x+9)⁷
find the derivative of the following function, simplify your answer
f(x)=(3x²-2x)e^x
e^x(3x²+4x-2)
find the derivative of the following function
-2x+5/(x²+5x)
if 20,000 is invested in a savings account offering 2.5% per year, compounded continuously, how fast is the balance growing after 5 years?
566.57
calculate the derivative of the function
ln[(-5x+7)(8x-3)]
(-5)/(-5x+7)+(8)/(8x-3)
find the exact location of all the absolute or relative extrema of the function with domain (-9,infiniti) x⁴-8x³
(6,-432)
the fencing on the east and west sides costs $4 per foot, and the fencing on the north and south sides cost only $2 per foot. I have a budget of 64.
maximize area=xy, 4x+8y=64
the consumer demand is given by the function q=108-p
a) at what price should tissues be sold to maximize revenue
b)what is the maximum revenue
a)54
b)2916
How much should be manufactured in order to minimize average cost?
1800
a study of us universities determined that enrollment was related to the annual cost of tuition by the following formula Q=11000-2.5p. in 1970 the average annual cost of tuition and fees was 2400 ,p=2400

a) determine the price elasticity of demand E=-dp/dp (p/q)
b) determine the value of elasticity when this tuition was is 2400
c) explain what is happening
a) 2.5p/11000-2.5p
b)1.2
for every 1% increase in tuition, enrollment drops by 1.2%
evaluate the integral ∫(16x³+(2/x)-4x+9)dx
4x⁴+2ln|x|-2x₂+9x+c
if f(0)=4 and the slope of the tangent line is 4x³+2x
x⁴+x²+4
the velocity of a projectile, in ft/sec is given by v(t)=72-32t

a)find an expression for the position s after a time t
b)given that s=10 and time t=0, find an expression for s in terms of t without any unknown constants
a)s(t)=72t-16t²+c
b) s(t)=72t-16t²+10
find f(x) if f(2)=1 and the tangent line at x has slope (x-1)e^(x²-2x)
.5e∧(x²-2x)+.5
∫6x(2x²+7)⁵dx
((2x²+7)⁶/4) +C
∫(5x/x²+6)dx
(5/2)ln|x²+6|+C
2xe^(-x)
(-2xe^-x)-(2xe^-x)+c
find the area of the region between f(x)=e^-x and g(x)=-2x on the domain [0,3]. show the expression you use, and evaluate by hand. leave your answer in exact form (no decimals)
10-e^-3
suppose your annual income is I(t)=30,000+5000t dollars per year, where t represents the number of years since you began your job while your annual expenses are
E(t)=20,000+4,000t dollar per year. find the area between the graphs of i(t) and e(t) (0<t<5)
62500
consumder surplus is defined as ∫₀^(qbar) (D(q)-pbar)dq
.50
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