Answer: (0, 2) and (6, 10)
Step-by-step explanation:
The acceleration is:
y = 7*sin( x*pi/4).
Over which interval is the acceleration increasing?
First, let's study the sin function:
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
Then we must choose one of the options that start with x = 0.
now it will stop increasing when:
θ = pi/2 = x*(pi/4)
x = 2.
So the acceleration is increasing in the segment (0,2)
And it will start increase again when:
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only deffined until x = 10, then
the correct option is: (0, 2) and (6, 10)
