Algebra Review
Find the domain of f(x)=x2-2x-3/x2-x-6
(-infinity,-2)U(02,3)U(3,infinity)
Find the lim as x-->-2 (x+2)/x^2-x-6
-1/5
Find the derivative of f(x). f(x)= 10(5x5+3x3+2)
f'(x)= 10(25x4+9x2)
Wendy's has a monthly fixed cost of $200,000 and a production cost of $18 for each baked potatoe produced. The product sells for $6.
a. what is c(x)
b. what is r(x)
c. what is p(x)
a. c(x)= 200,000 +18x
b. r(x)= 6x
c. p(x)= 6x-200,000-18x --> p(x)= -200,000- -8x
Find h(2) where h=g(f(x)) and f(x)=x+1 g(x)=2(x2-1).
7
Find the limit as x approaches infinity (3x^4-7x^3+6x-1)/2x^4-6x^2+7
3/2
What is the average rate of change in demand per week over the first 2 weeks.
(put answer in terms of the secant line!)
f(x)= -x2+6x+5 [0,3]
slope of the secant line= y=3x+5
The distance in meters covered by a skateboard after x seconds traveling down a ramp is given by y=-x3+(9/2)x2+12x
Find the skateboards acceleration at any time.
f''(x)= 6x-9
Let f(x)=x2-2 g(x)= x2-x-2 h(x)=2x
Find f-(g*h)
-2x3+3x2+2x
Find the limits for x-->-1 and x-->2
f(x)=
2x-1, x is less than or equal to -1
x, -1 <x less than or equal to 2
x^2-2, x>2
Limit x-->-1 DNE, b/c LHL does not equal RHL
Limit x--> 2= 2
Find the equation of the tangent line to the graph of f(x)=4x3+1 at x=1
y=12x-7
Find the points on the graph of f where the tangent line is horizontal. f(x)= x3-4x2
f'(x)=0*
points= (0,0)(8/3),(8/3)3-4(8/3)2)
What is the range of (5-x)1/2
[0,infinity)
Find the value of k so that the function is continuous everywhere.
f(x)= (2x^2+2x-4)/2x+4 x is not equal to -2
k if x=-2
k=-3
LHL=RHL*
Find the derivative of f(x)= 2/(x2-1)4
f'(x)= -16x/(x2-1)5
Nike produces shoes. The weekly cost for producing x shoes is c(x)= 8000+100x
a. find the marginal cost f(x).
b. find the average cost function.
c. find the marginal average cost function.
a. c'(x)= 100
b. average cost function= 8000/x +100
c. marginal average cost function= -8000/x2
-3/(a+h+4)(a+4)
Find the derivative using the limit definition of a derivative.
f(x)= 1/x-3
lim h-->0 -1/(x-3)^2
Find the derivative of f(x)= (x+1/x-1)2
f'(x)= -(4(x+1)/(x-1)3)
Let f(x)= (2/3)x3+x2-12x+6. Find the values of x for which f'(x)=-12
x=0,-1