Determine whether rolle's theorem can be applied to the function f(x) = x(x-2)^2 from 0 to 2

Rolle's theorem can be applies over the interval [0,2] for the given function f(x).

Step-by-step explanation:

We are given the following in the question;

The Rolle's theorem states that is

then, there exist c in the interval (a,b) such that

Condition:

Continuity of f(x)

Since f(x) is a polynomial function, it is continuous i the given interval [0,2].

Differentiability of f(x)

Since f(x) is a polynomial function, it is continuous i the given interval (0,2).

Equality of f(x)

Thus, Rolle's theorem can be applies over the interval [0,2] for the given function f(x).

73.0769230769% of the games were won

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.