Question

What is the shortest time interval during which it is guaranteed that a(t)=400 for some time t in the interval? justify your answer.

Answer 1

The lowest time interval for which it is guaranteed that A(t) = 400 is 70 ≤ t ≤ 90.

What is Intermediate value theorem?

• The intermediate value theorem in mathematics states that any value between f(a) and f(b) at some point within the interval can be assigned to f if it is a continuous function whose domain contains the interval [a, b].
• This theorem is used to demonstrate that a point can exist below or above a specific line. It can also be used to determine if a function is continuous or not by analyzing its continuity.

Calculation of time interval:

Because, A is diffrentiable, A, is continuous.

A(70) = 250<400<405 = A(90)

By the Intermediate Value Theorem, there must be at least one time t, for 70 ≤ t ≤ 90, such that A(t) =400.

Hence,  the shortest time interval during which it is guaranteed that A(t)=400 is 70 ≤ t ≤ 90.

Learn more about intermediate value theorem here:

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