Page 34 - Math SL HB Sem 2

f
4. The function/is defined by :x t-> -0.5x2 +2x+2.5.
(a) Write down

(D f'@);

(iD .f'(0).
(2)

(b) Let Nbe the normal to the curve at the point where the graph intercepts the y-axis. Show
that the equation of lf may be written as y = {).5r + 2.5.
(3)

Let g:.ru-0.5.r+2.5

(c) (i) Find the solutions of/(.r) = g (:).

(ii) Hence find the coordinates of the other point of intersection ofthe normal and the
curve.
(6)

(d) Let R be the region enclosed between the curve and N.

(D Write down an expression for the area of lQ.

(iD Hence write down the area oflR.
(s)
(Total l6 marks)

4