Show:
4.1
4.2
4.3
4.4
4.5 & 4.6
100
What is the formula for the Mean Value Theorem?
What is f’(c)=(f(b)-f(a)) / (b-a)
100
Use the Rolle’s Thereom to find xsinx [-4,4] *Hint: There are 3 X values
What is 2.03, -2.03, 0
100
What is the equation used in Newton's method?
What is X(n+1)= Xn- F(Xn)/F'(Xn)
100
FILL IN THE BLANKS: r(x)= _______________ from seeling x items c(x)= _______________ of producing x items p(x)= _________________(equation)- the profit from selling x items
What is revenue cost r(x)-c(x)
100
The Domain of y=n√x is [0,∞) if n is ________ and (-∞,∞) if n is _________.
What is even and odd
200
Where does the max/min occur?
What is When f’’(x) euqals 0
200
Find the POI for y=x^3-3x^2+4
What is (1,2)
200
x^2 +x-1=0 solve for one of the zeros using Newtons method.
What is Xn= -1.618033 or Xn= .6180339887
200
2. In Theorem 7, maximum profit (if any) occurs at a production level at which _______________=__________________
What is marginal revenue, marginal cost.
200
Functions such as f(x) = sin(x), f(x) = cos(x), or f(x) = tan(x) are called this. (Hint: not “Trigonomic functions”)
What is transcendental functions
300
Is x=-2 a max or min for y=2x^2+8x?
What is Min
300
Rolle’s Thereom to solve y=x^2+4x+5 [-3,-1]
What is x=-2
300
What is the Extreme Value Theorem?
What is (dy/dx)=0 (dy/dx)=DNE Endpoints
300
Suppose that r(x)=15x and c(x)=x^3+12x^2-7x+5 where x represents thousands of units. Is there a production level that maximizes profit? If so, what is it?
What is p(x)=15x-(x^3+12x^2-7x+5) = -x^3-12x^2+22x-5 p’(x)= -3x^2-24x+22 x= -8.83046 x=0.830459 r(-8.83)=-132.45 r(0.83)=12.45 c(-8.83)=313.971 c(0.83)= 9.04 r(x)-c(x)= -446.421 r(x)-c(x)=4.42 When x=0.83 maximum profit=4.42
300
Write an equation that combines both the chane of the area of a circle and the radius of a circle. A = πr²
What is dA/dt = (2πr)dr/dt
400
Find the max for f(x)=x^5-5x^4+5x^3+20
What is (1,21)
400
Use the Second Derivative Test to classify the critical points of y=(1/4)x^4-2x^3+6
What is x=0,6
400
Optimization is finding vales of x that give _____ or ______ values of f(x) where f is a function that models the real situation.
What is maximum, minimum
400
In the following: identify the inflection points, local minimum/ maximum values, and the intervals on which the graph is increasing, decreasing, concaving up, concaving down. y=^3root (1+x)
What is odd- (-infinity, infinity) y= (1+x)^(⅓) y’= ⅓ (1+x)^(-⅔) x (1) DNE @ -1 inc: (-infinity, infinity) dec: dne min:dne max:dne y’’= -2/9 (1+x)^(-5/3) DNE @ -1 Concave up: (-infinity, -1) Concave down: (-1, infinity) POI: dne
400
Show a complete graph, and identify the inflection points, local minimum/ maximum values, and the intervals on which the graph is increasing, decreasing, concaving up, concaving down. y=x+(25/x)
What is Answer: Increase: (-∞,-5) U (5,∞) Decrease: (-5,0) U (0,5) Max: DNE Min: (5,10) Concave Up: (0,∞) Concave Down: (-∞,0) POI: 0
500
Mean Value Thereom for y=x^3+3x^2-2
What is x= -1.57, -.42
500
Find the concavity of f(x)=3x^5-5x^3.
What is Concave up (-1/root2, 0)U(1/root2, infinity) concave down (-infinity, -1/root2)U(0, 1/root2)
500
A 10 by 15 in. sheet of paper is to have squares cut out of the corners so that the sides will fold to make an open box. Find the resulting maximum volume.
What is 0
500
Suppose that r(x)=15x and c(x)=x^3+12x^2-7x+5 where x represents thousands of units. Is there a production level that maximizes profit? If so, what is it?
What is p(x)=15x-(x^3+12x^2-7x+5) = -x^3-12x^2+22x-5 p’(x)= -3x^2-24x+22 x= -8.83046 x=0.830459 r(-8.83)=-132.45 r(0.83)=12.45 c(-8.83)=313.971 c(0.83)= 9.04 r(x)-c(x)= -446.421 r(x)-c(x)=4.42
500
How fast does the water level in a cylinder drop if it is being drained at a rate of 2 L/sec? (2000 cm3)
What is dV/dt = -2000 V = πr2h dV/dt = 2πr(dh/dt) -2000 = 2πr(dh/dt) -2000/2πr = (dh/dt) -2000/2πr cm/sec