# Question:Changing minimums over a two-variable function.

## Question:Changing minimums over a two-variable function.

Maple
I'm currently in first year calculus, so my knowledge is limited, please forgive me. I've been given an assignment, and a part of it has me rather stumped (the teacher likes to give out questions before she teaches you how to do them). We are given 3 single-variable functions (domain is 0 <= x <= 40): `h1 := x-> -5 * ( 1 - x^2 / 1600 ) * sin ( ( Pi * x ) / 1600 * ( x / 2 - 3 ) * ( x / 2 - 20 ) )^2;` `h2 := x-> -5 * ( 1 - x^2 / 1600 ) * sin ( ( Pi * x ) / 1600 * ( x / 2 - 6 ) * ( x / 2 - 20 ) )^2;` `h3 := x-> -5 * ( 1 - x^2 / 1600 ) * sin ( ( Pi * x ) / 1600 * ( x / 2 - 9 ) * ( x / 2 - 20 ) )^2;` And asked to find several things about them... that I have no problem with, however, the final part shows it as a two variable function. `h3d := (x,k) -> -5 * ( 1 - x^2 / 1600 ) * sin ( ( Pi * x ) / 1600 * ( x / 2 - k ) * ( x / 2 - 20 ) )^2;` She then asks to find the values of k where the number of minima in the single variable functions change... IE - h1 has 4 minimas, h2 has 3 minimas, and h3 has 2 minimas. I'd prefer a point in the right direction rather than a direct solution, but any help is greatly appreciated :)
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