Calculus help? Instantaneous rate?

Question

Here's the problem:
The cost (in dollars) of producing x units of a certain commodity is C(x)=5000+10x+0.05x^2. Find the instantaneous rate of change of C with respect to x when x=100

Answer 1

The function C(x) = 5000 + 10x + 0.05x^2.

instantaneous rate of change of C(x) : C ' (x).

Differentiate the function C(x) with respect to x.

C ' (x) = 10 + (0.05*2)x

C ' (x) = 10 + 0.1x.

when x = 100, C ' (x) = 10 + (0.1*100) = 10 + 10 = 20.

Therefore, the instantaneous rate of change of C with respect to x when x = 100 is 20 units.