1. The problem statement, all variables and given/known data
A parent takes their child to a water slide which is shaped similar to a portion of a parabola (see diagram). There is an elevator 3m from the edge of the pool. The elevator takes the rider to the top of the slide which is 19m above ground. The rider slides down and falls into pool from height of 1m. The parent (he is 2m tall) is standing 1m from the elevator and wishes to take a picture of the child when they are closest to the parent. What is the MIN. distance between parent and child?

3. The attempt at a solution
I sketched ou

Question

1. The problem statement, all variables and given/known data
A parent takes their child to a water slide which is shaped similar to a portion of a parabola (see diagram). There is an elevator 3m from the edge of the pool. The elevator takes the rider to the top of the slide which is 19m above ground. The rider slides down and falls into pool from height of 1m. The parent (he is 2m tall) is standing 1m from the elevator and wishes to take a picture of the child when they are closest to the parent. What is the MIN. distance between parent and child?

3. The attempt at a solution
I sketched ou

anonymous · Answer

the equation of the parabola is:
0.199445983x^2 - 3.789473684x + 19 = f(x)

anonymous · Answer

Taking the derivative of this function:
f'(x) = 0.398891966x - 3.789473684

anonymous · Answer

attachment

anonymous · Answer

I don't know what to do next....