Find the critical numbers of f(if any), find the open intervals, apply the first derivative test to identify all relative extrema, and use a graphing utility to confirm your results.
x^2-4x
What is x=2, dec(-inf,2) inc(2,inf) rel min (2,-4)
100
The sum of the first number and twice the second number is 108 and the product is a maximum.
What is 54 or 27?
100
find the anti-derivative of x+7 dx
What is .5x^2+7x+C?
100
using the fundamental theorem of calculus
6x [0,2]
What is 12.
200
What is the chain rule?
What is f'(g(x))*g'(x)?
200
find the critical numbers of f(if any), find the open intervals, apply the first derivative test to identify all relative extrema, and use a graphing utility to confirm your results.
-2x^2+4x+3
What is x=1, inc(-inf,1)dec(1,inf) rel max (1,5)
200
The product is 147 and the sum of the first number plus three times the second number is a minimum.
What is 21 or 7?
200
find the anti-derivative of x^3/2+2x+1 dx.
What is (2/5)x^(5/2)+x^2+x+C?
200
using the fundamental theorem of calculus (4x^3)-(3x^2) [1,3]
What is 54
300
Find of the derivative of arcsec(u).
What is u'/(abs(u)*sqrt(u^2-1))?
300
Determine the open intervals on which the graph is concave upward or concave downward.
(x^2+1)/(x^2-1)
What is concave up(-inf,-1)(1,inf)
concave down(-1,1)
300
A rectangular page is to contain 30 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.
What is 2+sqrt(30) * 2+sqrt(30)?
300
Find the anti-derivative of 2sinx -5e^x dx.
What is -2cosx-5e^x+C.
300
Using the limit definition 3x+10 [-1,5]
What is 96
400
What is the derivative of ln((x(x^2+1)^2)/sqrt(2x^3-1)).
What is 1/x+4x/(x^2+1)+3x^2/(2x^3-1)?
400
Determine the open intervals on which the graph is concave upward or concave downward.
(-3x^5+40x^3+135x)/270
What is concave up (-inf, -2) (0,2)
concave down (-2, 0) (2,inf)
400
A farmer plans to fence a rectangular pasture adjacent to a river. the Pasture must contain 245,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What dimensions will require the least amount of fencing?
What is 700*350?
400
find the anti-derivative of (x+6)/sqrt(x) dx.
What is (2/3)x^(3/2)+12x^(1/2)+C?
400
using the limit definition
6x(4-x)^2 [0,4]
What is 128
500
find dy/dx by implicit differentiation.
xe^y-10x+3y=0
What is (10-e^y)/(xe^x+3)?
500
find the points of inflection and discuss the concavity of the graph of the function.
y=e^-(3/x)
What is point of inflection (3/2, e^-2)
concave upward(-inf, 0)(0,3/2)
concave downward (3/2, inf)
500
A solid is formed by adjoining two hemispheres to the ends of a right circluar cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.