Question

The Cost (in dollars) of producing x units of a certain commodity is C(x) = 500 + 10x + 0.005x
2
i. Find the average rate of change of C with respect x when the production level is from x = 100 to
x = 105 units. [2]
ii. Find the instantaneous rate of change of C with respect to x when x = 100.

Answer 1

Where the average change=∆y/∆x

marginal change in production=(y2-y1)/(x2-x1)

At x=100

C(x) = 500 + 10x + 0.005x²?

If yes then this is all you need to do


C(100)=500+10(100)+0.005(100)²

=500+1000+50=1550

at x=105
C(105)=500+10(105)+0.005(105)²
=500+1050+55.125
=1,605.125

Y2=1605.125 ,y1=1550
X1=100 X2=105

average change=∆y/∆x=(1605.125 -1550)/(101-100)=55.125

Instant change of x would respect to c just say

C(x)=500 + 10x + 0.005x²?

C'(x)=10+2x(0.005)

C'(x)=10+0.01x

Where x=100
C'(100)=10+0.01(100)=10+1
=11

Answer 2

Correction

average change=∆y/∆x=(1605.125 -1550)/(105-100)=55.125/5=11.025