The vertical height HHH of a roller coaster track, in metres, is modeled by the equation H=H(x),x>0H = H(x), x > 0H=H(x),x>0, where xxx is the horizontal distance from a reference point. The track passes through the point P(4,10)P(4, 10)P(4,10).
Given that
dHdx=3x2−8x \frac{dH}{dx} = \frac{3x^2 - 8}{\sqrt{x}} dxdH=x3x2−8Find the equation of the tangent to the track profile at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c, where mmm and ccc are integers to be found.
Find the function H(x)H(x)H(x).
