fast is marginal cost changing

If C(x)=2.0x^2+9x+200 is a cost function, how fast is marginal cost changing when x=100?

I took the derivative and got 4x+9 and plugged the 100 in and got 409. However, I was told that in order to find how fast the marginal cost is changing i have to do the second derivative. I am not sure which answer is right.
Can someone explain to me whether i take have to find the second derivative in order to solve this questions.

Please and thank you

Quote:

---

Originally Posted by happy8588

If C(x)=2.0x^2+9x+200 is a cost function, how fast is marginal cost changing when x=100?

I took the derivative and got 4x+9 and plugged the 100 in and got 409. However, I was told that in order to find how fast the marginal cost is changing i have to do the second derivative. I am not sure which answer is right.
Can someone explain to me whether i take have to find the second derivative in order to solve this questions.

Please and thank you

---

Yes, it should be the second derivative. the first derivative is the marginal cost. to find the rate at which that is changing, you would need to differentiate it (take another derivative).