Mathematics

Problem

A straight line

y=3x+c

and the parabola

y=x^{2}

bound a region between

x=0

and

x=3

. a. (i) State the inequality that

c

must satisfy so that the line remains above the parabola for every

x

[0,3]

. b. (ii) Derive an expression, in terms of

c

, for the area of the region enclosed by the two curves on

[0,3]

. c. (iii) Given that this area equals

27

square units, determine the value of

c