Please help me!
Find the formula for the function of the form w(x)= Asin(Bx)+C with an (i) a maximum (3,6),(i) a minimum at (-9,6), and (iii) no critical points between these two points
3 answers
6 sin(pi/6 x) +0
how can it have a max and a min at y=6, and no critical points in between?
By Rolle's Theorem, there must be a point in the interval where w'(x) = 0
But that is another critical point.
And anyway, since the amplitude A is 1/2 the difference between the max and the min, A=0, right?
But the proposed solution is bogus, since
If w(x) = 6 sin(pi/6 x) + 0 then
w(3) = 6 * 1/2 + 0 = 3
By Rolle's Theorem, there must be a point in the interval where w'(x) = 0
But that is another critical point.
And anyway, since the amplitude A is 1/2 the difference between the max and the min, A=0, right?
But the proposed solution is bogus, since
If w(x) = 6 sin(pi/6 x) + 0 then
w(3) = 6 * 1/2 + 0 = 3
so let's say that there is a maximum at (3,6) and a minimum at (-9,-6)
The A = (6+6)/2 = 6 and C = (6-6)/2 = 0
But now you have to have a phase shift, so that means that since the period is 2(3+9) = 24
w(x) = 6cos(pi/12 (x-3)) = 6sin(pi/12 (x+3))
The A = (6+6)/2 = 6 and C = (6-6)/2 = 0
But now you have to have a phase shift, so that means that since the period is 2(3+9) = 24
w(x) = 6cos(pi/12 (x-3)) = 6sin(pi/12 (x+3))