Froggy Jumps
Application of Differentiation adapted into a trivia game
1
which point is undefined?
2
Given the function, find coordinate of stationary point using Second Derivative Test and determine the nature of the points.
3
Find the equation of the tangent to
4
The volume of a sphere is increasing at some rate.Find the rate at which the radius is increasing when the radius is 4cm.
5
A water tank in the shape of an inverted circular cone has a radius of 20m and height of 40m. Water is being pumped into the tant at some rate. Calculate the rate of increase of the height of the water when the depth of the water is 10 m.
6
A rectangle has a fixed perimeter of 100 meters. What is the maximum area?
7
A farmer wants to fence a rectangular plot and divide it into two equal sections with a fence parallel to one side, use 300 meters of fencing. What is the maximum of total area?
8
A 40 cm by 40 cm metal sheet is folded into an open top box by cutting squares from corners. What size square should be cut to hold maximum volume?
9
What is the gradient of the tangent line to a curve defined by?
10
What do we call a point where f'(x) = 0 and the function changes from increasing to decreasing?
11
Which condition indicates a point of inflection?
12
In The First Deriavative Test; ehich scenario identifies a relative minimum at x = a
13
A cylindrical can has a total surface area .Find the radius that gives the maximum value.
14
Based on the graph, what type of function is it?
15
Find the point of inflection for the function,
16
A cuboid storage is designed to have an open at the top and square base. The base has side length of x cm and the height of h cm. It has a total volume of 36.
Write x in term of h
17
the equation stated equals to....
18
Find the stationary point for the function
19
Find the maximum height
20
Find velocity of particle at t=2
21
Find the equation of the tangent and normal lines at point where x=2?
22
Find the maximum point of the function.
23
Find the point of inflection of
24
A rectangular garden with an area . What dimensions give the smallest perimeter?
25
The area of circle is increasing at a rate. What is the radius when r=5cm?
26
What is the derivative of a function used to find at a specific point on a graph ?
27
What does it means if the first derivative of a function is positive over an interval ?
30
If a function has a critical point, what must be true about its derivative at that point ?
31
Find the local maximum of
32
Determine the inflection point of
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