The period of a pendulum is the time the pendulum takes to swing back and forth one full time. The function I = 0.81t^2 relates
1 answer:
You might be interested in
Answer:
a)
b)
Step-by-step explanation:
The first step to solve this question is finding the roots of the derivative of x.
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:
So
Finding the roots:
Simplifying by -3
So
Then
So the function can be divided in three intervals.
They are:
Less than -1
Between -1 and 5
Higher than 5
In which it increases and which it decreases?
Less than -1
Lets find the derivative in a point in this interval, for example, -2
Positive.
So in the interval of , the function increases.
Between -1 and 5
Will choose 0.
Negative.
So in the interval of , the function decreases.
Higher than 5
Will choose 6.
Positive
So in the interval of , the function increases.
(a) Find the interval on which f is increasing.
Using interval notation
b) Find the interval on which f is decreasing.