my car's yearly mileage is 10,000 and the average cost per gallon is $2.48
how do I write the cost function C(x)=?
I put it as C(x)=10000+2.48x is this correct?
please help

Let x be the number of miles you can cover with one gallon.

The number of gallons you use will depend on how many miles you run with one gallon.

How many gallons do you use? It's \frac{10,000}{x}

And now, for 1 gallon, you pay $2.48. For 10 000/x gallons, you'll pay:

\frac{10,000}{x} \times 2.48

So,

C(x) = \frac{10,000}{x} \times 2.48 = \frac{24 800}{x}

thanks, but if I took the derivative of the equation wouldn't it be just C'(x)=10000. Where would I plug in my x. e.g. it says in the question, find C'(x) when x=10.

No, look carefully at the power of x there. Since x is the denominator, it's power is -1.

C(x) = 24800 x^{-1}

C'(x) = -24800 x^{-2}