# Thread: finding formula with max and min

1. ## finding formula with max and min

Find a formula for the following function.
A curve of the form y = Acos(Bx) + C with a maximum of (0 , 13), a minimum of (4 , 10) and no critical points between these two points.

A=
B=
C=

I think im going about this wrong. i found the derivative and tired solving for the different constants but for some reason it isnt working

2. I don't think you need to your calculus for this problem. Just understanding how the parameters A,B, and C affect the shape of the graph of the cosine function should suffice. C is the amount the graph is shifted up and or down while A is the amplitude of the graph (the amount the function goes up from C and down from C).

So draw a standard cosine graph. Shifting the graph up by 1 amounts to adding 1 to the cosine function, in other words setting C = 1.
In this shifted cosine function the graph oscillates between 2 and 0 instead of 1 and -1.

Note that the value of C is the midpoint between 2 and 0 the max and the min, this is not an accident.

The value of B changes how quickly the function oscillates (a correct choice for this value will ensure that the correct number of critical points appear in the interval (0,4))