A cyclist is competing in a tournament. he is currently in a very hilly part of the course. for his current hill his height in meters over time in minutes is modelled by the function f(x)=-0.00075x^2. - 0.5825x + 17.269. estimate the cyclists instantaneous rate of change and give his direction at x=100.
don't really understand this question any help would be amazing
To estimate the rate of change, find the slope joining two points close to each other on the graph. You can use any small value of h, say 0.1, and then calculate
∆y/∆x = (f(100.1)-f(100))/0.1 = (-48.55+48.48)/0.1 = -0.7 m/min
I have no idea what his direction would be, but since his height is decreasing, I;d say downhill.