MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The function f is defined by f:x↦−0.5x2+2x+2.5.
Let g:x↦−0.5x+2.5.
(1) Write down f′(x).
(2) Write down f′(0).
(3) 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.
(4) Find the solutions of f(x)=g(x).
(5) Hence find the coordinates of the other point of intersection of the normal and the curve.