# Tutor profile: Nora C.

## Questions

### Subject: French

Easier: Translate this phrase from French to English: We ate dinner. Harder: Translate this phrase to French: It is necessary that you go to the meeting.

Easier: Nous avons dîné. Harder: Il faut que vous alliez au rendez-vous. This phrase requires the subjunctive tense.

### Subject: Calculus

In economics, marginal cost is defined as the derivative of the cost function. If the cost of calculus textbooks can be defined as $C(x)=10+2x^2+3x^3$, what is the marginal cost? Evaluate the marginal cost at $x=2$.

Marginal cost is $C'(x)$, the derivative. By calculating this, we see $C'(x)=4x+9x^2$. Next, we evaluate $C'(x)$ at $x=2$. We get $C'(2)=4\cdot 2 + 9\cdot 2^2$, or $C'(2)=8+36=44$.

### Subject: Algebra

Solve the following equation by factoring and by the quadratic equation. $$y=x^2-3x+2$$ Which is easier?

By factoring, we see that $y=(x-1)(x-2)$, so $x=1$ and $x=2$. With the quadratic equation, we have $x=\frac{3\pm\sqrt{9-4\cdot 1\cdot 2}}{2}=\frac{3\pm\sqrt{1}}{2}=\frac{3\pm 1}{2}$, so $x=\frac{4}{2}$ or $x=\frac{2}{2}$. We see $x=2$ and $x=1$. Both methods yield the same result, but using factoring is easier.

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