WorksheetsCalculus Optimization Challenge
Total questions: 10
Worksheet time: 5mins
What is the maximum value of the function f(x) = -2x^2 + 4x + 1?
4
1
2
3
Find the minimum point of the function g(x) = x^3 - 3x^2 + 4.
(0, 4)
(2, 0)
(-1, 6)
(√2, 2 - 2√2)
Determine the critical points of the function h(x) = 3x^4 - 8x^3 + 6.
x = 1
x = -2
x = 0, x = 2
x = 3
Using calculus, find the dimensions of a rectangle with a perimeter of 20 that maximizes the area.
2, 8
5, 5
3, 7
4, 6
A farmer wants to fence a rectangular area using 100 meters of fencing. What dimensions will maximize the area?
25 meters by 25 meters
20 meters by 30 meters
15 meters by 35 meters
10 meters by 40 meters
Find the point on the curve y = x^2 + 2x that is closest to the point (1,0).
(0, 0)
(1, 1)
(2, 4)
(-1, 1)
What is the maximum profit if the profit function is given by P(x) = -5x^2 + 50x - 100?
30
20
15
25
Using the first derivative test, determine the local maxima and minima of the function j(x) = x^4 - 8x^2 + 16.
Local maximum at x = 2, local minimum at x = 0.
Local maximum at x = 0, local minimum at x = -2.
Local maximum at x = -2, local minimum at x = 2.
Local maximum at x = 1, local minimum at x = -1.
Find the dimensions of a box with a square base that has a volume of 500 cubic meters and minimizes the surface area.
Base: 5 meters, Height: 20 meters
Base: 10 meters, Height: 5 meters
Base: 15 meters, Height: 2.22 meters
Base: 8 meters, Height: 12.5 meters
If the revenue function is R(x) = 100x - 0.5x^2, find the number of units sold that maximizes revenue.
100
150
50
200
