He wondered what the equation of such a perfect roller coaster
would be. As he dreamed that night, he discovered the following equation:
๐ป(๐) = ๐๐
3 + ๐๐
2 + ๐๐ + ๐ would work, where H(d) represents the height above the
ground, and d represents the horizontal distance the coaster has travelled.
In order to make his perfect roller coaster, he wanted the following to be true.
๐. ๐กโ๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐ก๐๐ ๐๐ข๐ ๐ก โ๐๐ฃ๐ ๐ ๐๐๐๐๐ ๐๐๐ฅ๐๐๐ข๐ ๐๐ก ๐กโ๐ ๐๐๐๐๐ก ๐คโ๐๐ ๐ =1/2
๐๐. ๐โ๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐ก๐๐ ๐๐ข๐ ๐ก โ๐๐ฃ๐ ๐ ๐๐๐๐๐ min ๐คโ๐๐ ๐ = 2 , โ = 0.5
๐๐๐. ๐โ๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐ก๐๐ ๐๐ข๐ ๐ก โ๐๐ฃ๐ ๐ ๐๐๐๐๐ก ๐๐ ๐๐๐๐๐๐๐ก๐๐๐ ๐๐ก ๐กโ๐ ๐๐๐๐๐ก ๐คโ๐๐ ๐ = 1.25
๐๐ฃ. ๐โ๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐ก๐๐ ๐ ๐ก๐๐๐ก๐ ๐๐ก ๐ โ๐๐๐โ๐ก ๐๐ 1 ๐ ๐๐๐๐ฃ๐ ๐กโ๐ ๐๐๐๐ข๐๐
Determine any such equation satisfying the above using methods of calculus only! Your
solutions must be neat and organized.
1 answer
so write those equations to solve for a,b,c
also, you know e = 1.25
Do that and you will wind up with
y = 4x^3-15x^2+12x+1
This same problem has been posted before. See Similar Questions below, under "calculus"