Q.(MCQ) If the total cost function is $TC = Q^2 + 40$, the Marginal Cost at $Q=6$ is:

Marginal Cost is $\dfrac{d(TC)}{dQ}$; differentiating $Q^2+40$ gives $2Q$, and substituting $Q=6$ gives $12$. …

Given: $TC=Q^2+40$; find $MC$ at $Q=6$ and choose the correct option among (a)-(d).

Step 1 — Differentiate $TC$: $\dfrac{d(TC)}{dQ} = 2Q+0 = 2Q$ (the constant $40$ differentiates to zero).

Step 2 — Substitute $Q=6$: $MC(6) = 2(6) = 12$, which is option (b).

Step 3 — Why the other options are wrong: (a) $6$ mistakenly reports $Q$ itself rather than $2Q$ — it drops the coefficient $2$ that the power rule produces. (c) $46$ is the value of $TC$ itself at $Q=6$ ($36+40=76$... in fact even $TC(6)=76$, so a student who confuses (c) with $TC$ has miscalculated $TC$ too — the more likely trap for (c) is treating $Q+40=46$ literally, forgetting to square $Q$ first and forgetting to differentiate at all). (d) $76$ is $TC(6)$ itself ($6^2+40=76$) — this is the value of TOTAL cost at $Q=6$, not MARGINAL cost; a student who selects this has confused the two concepts entirely, exactly the common mi …

Reporting the TOTAL cost $TC(6)=76$ as if it were the Marginal Cost — Marginal Cost is always the DERIVATIVE of total cost, evaluate …