What is the derivative of F(x) = 4x^3 + 3x^2 + 8x + 9
100
It can be applied and f'(3/2) = 0
Determine if Rolle's theorem can be applied, find all values of c in the open interval (a,b) such that f'(c) = 0
F(x) = -x^2 + 3x, [0,3]
100
2 tan y - 5e^y + C
Find the indefinite integral 2 sec^2 (y) - (5e^y) dy
100
L=W= 4 sqrt (2) ft
Find the length and width of a rectangle that has the given area and minimum perimeter
Area = 32 square feet
100
(6x) dx [0,2] = 12
Evaluate the definite integral
(6x) dx [0,2]
200
F'(x) = 1/ 2 square root (x-3)
What is the derivative of the function
F(x) = square root (x-3)
USE THE LIMIT DEFINITION
200
f'(1/sqrt (3)) = 3
f-(-1/sqrt (3) = 3
Determine whether the Mean Value theorem can be applied to f on the closed interval [a,b]. If yes, find all values of c in the open interval (a,b) such that f'(c) = (f(b) - f(a))/b - a
F(x) x^3 + 2x, [-1,1]
200
68
Given
(x^3) dx = 60 on [2,4]
dx = 2 on [2,4]
Evaluate (x^3 + 4) dx on [2,4]
200
W = (5 sqrt (2))/2
L= 5 sqrt (2)
A rectangle is bounded by the x-axis and the semicircle
y= sqrt (25 - X^2)
What length and width should the rectangle have so that it's area is a maximum
200
(3/x^2 - 1) dx [1,2] = 1/2
Evaluate the definite integral
(3/x^2 - 1) dx [1,2]
300
(f^-1)'(a) = 1/5
Verify that F(x) = x^3 + 2x - 1 has an inverse
Use the function and the real number a = 2 to find (f^-1)'(a)
300
Rolle's Theorem does not apply
Determine if Rolle's theorem can be applied, find all values of c in the open interval (a,b) such that f'(c) = 0
f(x) = 2 + arcsin(x^2 - 1), [-1,1]
300
Area = 16
Given
(4 - |x|) dx on [-4,4]
Find the area using a geometric formula
300
700 x 350 m
A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 245,000 square meters. No fencing is needed along the river. What dimensions will require the least amount of fencing?
L1 = x, L2 = river, W1= y, W2 = y
300
(1 - sin^2 x) / (cos^2 (x)) dx [0,pi/4] = pi/4
Evaluate the definite integral
(1 - sin^2 x) / (cos^2 (x)) dx [0,pi/4]
400
y= 8/5x - 7/5
Find an equation of the tangent line to the graph of f at the given point
F(x) = square root (2x^2 - 7)
Point (4,5)
400
1.5 seconds
Use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.
s(t) = -4.9^2 + 300
400
0
Evaluate the Integral using the limit definition
(x^3)dx [-1,1]
The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area.
400
A = 1
Determine the area of the region
y= cos x from [0,pi/2]
500
Int = (0,0) and (27/8,0)
Inflection = (0,0)
No asymp
Extrema (1,1)
Identify intercepts, relative extrema, inflection points, and asymptotes
Y = 3x^2/3 -2x
500
V = 0 for t in (1,2)
t= 3/2 sec
According to Rolle's Theorem what must the velocity be at some time in the interval (1,2)? Find that time.
F(t) = -16t^2 + 48t + 6
500
166.67
Evaluate the integral using the limit definition
(25 - x^2) dx [-5,5]
500
r = 1.50
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic cm. Find the radius of the cylinder that produces the minimum surface area.
500
(e^x + sin x) dx on [-1,1] = e - e^-1
Evaluate the definite integral
(e^x + sin x) dx on [-1,1]