The function f is defined by f:x↦−0.5x2+2x+2.5.
Let g:x↦−0.5x+2.5.
a. Write down f′(x).
b. Write down f′(0).
c. Let N be the normal to the curve at the point where the graph intercepts the y-axis. Show that the equation of N may be written as y=−0.5x+2.5.
d. Find the solutions of f(x)=g(x).
e. Hence find the coordinates of the other point of intersection of the normal and the curve.