Mathematics

Problem

Let

p(x)=x^{2}

and

q(x)=5x+7

. a. (i) Derive a simplified expression for the average rate of change of

p

between

x=a

and

x=b

. b. (ii) Show that this expression can be written as

a+b

, and hence comment on whether it is constant for all intervals. c. (iii) Find the average rate of change of

q

between

x=a

and

x=b

and prove that it is independent of

a

and

b

. d. (iv) Using your results in parts (ii) and (iii), state two conclusions that distinguish linear and quadratic functions with respect to their rates of change.

Browse the problem library