# Thread: Final Questions for Practice Test

1. ## Final Questions for Practice Test

Find the equation of the tangent line for the function f(x) = x^2 + 1 at point (3, 10).

A. y = 6x - 8

B. y = -6x+8

C. y = 6x+8

D. None of these

Question 14.

If I divide my eldest cousin's age by 3 and subtract 4, i get the same result as when I divide his age by 6. What is his cousin's age?

A. 22yrs

B. 24yrs

C. 30yrs

D. None of these

2. Question:

If we have the function $\displaystyle f(x) = x^2 + 1$ our derivative would be $\displaystyle f'(x) = 2x$. If we need our slope at point (3, 10) we plug the x into our derivative, we get: $\displaystyle f'(3) = 2 \cdot 3$. Which results in $\displaystyle 6$.

Now we need to find some equation that crosses the point (3, 10) with the following form $\displaystyle y(x) = ax + b$, we can do this by plugging in our coordinates and our slope: $\displaystyle 10 = 3 \cdot 6 + b$, which gives us: $\displaystyle -8$. Our equation would look like: $\displaystyle y(x) = 6x - 8$. Which is A.

Question 14:

I would say he is 24. Because $\displaystyle \frac{x}{3} - 4 = \frac{x}{6}$.

Now solve the equation for x:

$\displaystyle \frac{x \cdot 2}{3 \cdot 2} - \frac{4 \cdot 6}{6} = \frac{x}{6}$ (note: I'm doing this so our denominator is the same on both sides)

$\displaystyle 2x - 24 = x$

$\displaystyle 2x - x = 24$

$\displaystyle x = 24$