Consider the following equation. cos x = x3 (a) Prove that the equation has at least one real root. f(x) = cos x − x3 is continu
ous on the interval [0, 1], f(0) = 0, and f(1) = cos 1 − 1 ≈ −0.46 0. Since 0 −0.46, there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x − x3 = , or cos x = x3, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root.
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Answer:
The rate rate of change of radius is inches per second when the diameter is 12 inches.
The radius is changing more rapidly when the diameter is 12 inches.
Step-by-step explanation:
Consider the provided information.
A spherical balloon is being inflated at a rate of 3 cubic inches per second.
The volume of sphere is
Differentiate the above formula with respect to time.
Substitute the respective values in the above formula,
The rate rate of change of radius is inches per second when the diameter is 12 inches.
When d=16
Thus, the radius is changing more rapidly when the diameter is 12 inches.