The profile of a section of a rollercoaster is given by : h(x)=(2500+500sin(100pix))/x. h is the height of track and x is the horizontal position. Is the track going upwards or downwards at x=250m?
Ans: to solve this can we just find the first derivative and sub in 250 for value of x and if its positive then its moving upwards and if negative its moving downwards. Or do we also need to find the second derivative to see if it is a point of inflection?
h' is all you need.
h" indicates whether it's on a hill (concave down) or in a bowl (concave up)