ANSWERS AND EXPLANATIONS TO SECTION I
1. B First, take the antiderivative: ∫ cos(2t) dt = sin(2t).
Next, plug in x and for t and take the difference: sin(2x) − sin.
This can be simplified to .
- D In order to find the inflection point(s) of a polynomial, we need to find the values of x where
its second derivative is zero.
First, we find the first and second derivative.
= 3x^2 − 30x + 33
= 6x − 30
Now, let’s set the second derivative equal to zero and solve for x.
6 x − 30 = 0; x = 5
In order to find the y-coordinate, we plug in 5 for x in the original equation.
y = 5^3 − 15(5^2 ) + 33(5) + 100 = 15
Therefore, the coordinates of the point of inflection are (5, 15).
- B We need to use implicit differentiation to find .
6 x − + 3 = 0
6 x − 2x − 2 y + 3 = 0
Now, if we wanted to solve for in terms of x and y, we would have to do some algebra to
