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A Toblerone bar comes in packaging that forms a triangular prism with equilateral triangles at both ends. If the volume of the package is 20cm3, determine the dimensions of the package that give a minimum surface area. V = 1/2bhl, S = bh + 3bl
The number of people attending a concert is represented by 9000(75-x), where x is the cost of the ticket in dollars. What ticket price will maximize the total revenue of the concert?
The cost in dollars of producing x headphones is
C(x) = 2000 + 150x – 0.1x2
a. Calculate the average cost of producing 250 headphones.
b. Calculate the marginal cost of producing the 250th headphone.
The radioactive isotope carbon-10 has a half-life of 20 seconds.
a. How much time is required so that only 1/16 of the original amount remains?
b. Find the rate of decay at this time.
Given y = 2x – 4 / x+1
a. State whether the function is odd or even.
b. Find the vertical and horizontal asymptotes.
c. Find the x- and y-intercepts.
d. Find y’ and y’’, intervals of increase and decrease, inflection points and concavity.
e. Sketch the function.
For the function f(x) = 4x3 – x2– 3, determine
a. The intervals of increase or decrease
b. The location of any maximum or minimum points c. The intervals of concavity up or down
d. The location of any points of inflection
Determine all the points on the curve y = 2x3 + 3x2 - 18x + 3 where the slope of the tangent line is -6.
A. Find the area underneath the given curve.
1.) y= -2x² + 8
from x=0 to x=1
2.) y= -x² + 7
from x=0 to x=1
B. Find the area enclosed by the given curve, the x-axis, and the given lines.
1.) y= -1/3x² + 10
from x=1 and x=3
2.) y= x³ - 8
from x= -1 to x =2
C. Find the area bounded by the given curve and line.
1.) y= x² + 3 and y= 7
2.) y= 2x² and y= 4x + 6
3.) y= -x² + 4x and y= x²
4.) y= x³ -6x² + 8x and y= x² -4x
D. Find the area bounded by y=2; y=√x+2; and y=2 - x.
A. Find the area underneath the given curve.
1.) y= -2x²+8
from x=0 to x=1
2.) y= -x²+7
from x=0 to x=1
B. Find the area enclosed by the given curve, the x-axis , and the given lines.
1.) y=-1/3 x² + 10,
from x=1 and x=3
2.) y= x³-8
from x=-1 to x=2
C. Find the area bounded by the given curve and line.
1.) y= x² + 3 and y=7
2.) y= 2x² and y= 4x + 6
3.) y = -x² + 4x and y= x²
4.) y= x³ - 6x² + 8x and y= x² - 4x
Find the area bounded by y=2; y=√x+2; and y=2-x.
