A toy ball in the shape of a sphere expands and contracts. When it is completely closed, it has a diameter of 12.5 inches.Find
1 answer:
The volume of the sphere is
Explanation:
Given that the diameter of the toy ball is 12.5 inches
We need to determine the volume of the toy ball.
The radius of the toy ball is given by
Thus, the radius of the toy ball is 6.25 in
The volume of the sphere can be determined using the formula,
Substituting the values, we get,
Multiplying, we get,
Substituting , we have,
Simplifying, we get,
Thus, the volume of the sphere is
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Answer:
relative maximum: x = 1
relative minimum: x = 7
Step-by-step explanation:
Critical points:
Values of x for which f'(x) = 0.
Second derivative test:
For a critical point, if f''(x) > 0, the critical point is a relative minimum.
Otherwise, if f''(x) < 0, the critical point is a relative maximum.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that
, given by the following formulas:
In this question:
Finding the critical points:
Simplifying by 3
So
Second derivative test:
The critical points are x = 1 and x = 7.
The second derivative is:
Since f''(1) < 0, at x = 1 there is a relative maximum.
Since f''(x) > 0, at x = 7 there is a relative minumum.