If we multiply through by 8, we get 8y + 8 = 9x − 18 or 9x − 8y − 26 = 0.
- D Acceleration is the second derivative of position with respect to time (velocity is the first
derivative).
The first derivative is v(t) = 3t^2 − 12t + 9.
The second derivative is a(t) = 6t − 12.
Now we simply plug in t = 4 and we get a(4) = 24 − 12 = 12.
- D The derivative of an expression of the form au, where u is a function of x, is
au = au (ln a)
Here we get
3 πx = 3πx (ln 3)π
- D In order to find the average value, we use the Mean Value Theorem for Integrals, which says
that the average value of f(x) on the interval [a, b] is f(x) dx.
Here we have .
Evaluating the integral, we get ln x = ln e − ln 1 = 1. Therefore, the answer is .
- C We just use the Chain Rule three times.
f′(x) = 2 sin x cos x = sin 2x
f′′(x) = 2 cos 2x
f′′′(x) = −4 sin 2x
- B First, we need to find using implicit differentiation.
