Final Questions for Practice Test

Question:

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

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

Question 14:

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

Now solve the equation for x:

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

$2x - 24 = x$

$2x - x = 24$

$x = 24$

Correct answer would be B.