I know this question, has been asked, but I have 2 question.
First :
3a*2^2 + 2b*2 + c = 0
3a(1/2)^2 + 2b(1/2) + c = 0
How do the equations equal zero when, H'(1/2) < 0, H'(2) > 0, and H'(2) = 1/2
Second:
6a(5/4) + 2b = 0
3a*2^2 + 2b*2 + c = 0
3a(1/2)^2 + 2b(1/2) + c = 0
how do these three systems of equations produce H(d) = 4d^3 - 15d^2 + 12d + 1, I'm confused
The Question:
The given function H(d) = ad^3 + bd^2 + cd + e represents a roller coaster, where H(d) represents the height above the ground, and d represents the horizontal distance the roller coaster has travelled.
Make it so the following parameters are true:
1) The roller coaster must have a local maximum at the point when d =(1)/2
2) The roller coaster must have a local minimum when d = 2 , h = 0.5
3) The roller coaster must have a point of inflection at the point when d = 1.25
4) The roller coaster starts at a height of 1 m above the ground.
You say
1) The roller coaster must have a local maximum at the point when d =(1)/2
so, h'(1/2) = 0
2) The roller coaster must have a local minimum when d = 2 , h = 0.5
so, h'(2) = 0
3) The roller coaster must have a point of inflection at the point when d = 1.25
so, h"(5/4) = 0
That allows you to solve for a,b,c
If you go back to the original post, you will find that it did not say
H'(1/2) < 0, H'(2) > 0
It said H''(1/2) < 0, H''(2) > 0
so you can verify whether the extrema are max or min.