Question

How do I find the marginal cost of the following: C(Q)= 50+10Q+2Q^2

Answer 1

Marginal Cost function for the curve: C(Q)= 50+10Q+2Q^2 is given by the differential for this curve with respect to the quantity..
The differential of an expression with respect to the variable x , say x^n would be n times x raised to power n-1, i.e. n(x^(n-1))

The differential of the constant term would be Zero.
Hence, for C(Q)= 50+10Q+2Q^2

Its Differential, i.e. dC/dQ = 4Q + 10
Hence, for a total cost function, marginal cost can be obtained by finding its differential or slope with respect to the variable Q.

Hence, MC=  4Q + 10

Let me know in comments if you have any questions.