Question

Calculus I Quiz 7 Form B Sec 3.5 & 3.6 Name: 1. The graph of $f(x)$ is given below. Fill in the blanks using the words: positive, negative, zero, increasing, decreasing, constant, concave down, concave up as needed. $f'(a)$ is because $f(x)$ is when $x = a$. $f''(a)$ is because $f(x)$ is when $x = a$. 2. The traffic speed $S$ (mph) on a two-lane road is a function of the traffic density $Q$ (number of cars per mile) and is given by the formula $290Q^{-1} - 0.04Q + 31$ for $60 \le Q \le 400$. Calculate the following: $\frac{dS}{dQ} = $ $\frac{d^2S}{dQ^2} = $ 3. Find an equation of the tangent line to $f(x) = x\cos(x)$ at $x = \frac{\pi}{4}$.

          Calculus I
Quiz 7 Form B
Sec 3.5 & 3.6
Name:
1. The graph of $f(x)$ is given below. Fill in the blanks using the words: positive, negative,
zero, increasing, decreasing, constant, concave down, concave up as needed.
$f'(a)$ is ______ because $f(x)$ is ______ when $x = a$.
$f''(a)$ is ______ because $f(x)$ is ______ when $x = a$.
2. The traffic speed $S$ (mph) on a two-lane road is a function of the traffic density $Q$ (number
of cars per mile) and is given by the formula $290Q^{-1} - 0.04Q + 31$ for $60 \le Q \le 400$.
Calculate the following:
$\frac{dS}{dQ} = $
$\frac{d^2S}{dQ^2} = $
3. Find an equation of the tangent line to $f(x) = x\cos(x)$ at $x = \frac{\pi}{4}$.

Calculus I
Quiz 7 Form B
Sec 3.5 3.6
Name:
1. The graph of f(x) is given below. Fill in the blanks using the words: positive, negative,
zero, increasing, decreasing, constant, concave down, concave up as needed.
f'(a) is because f(x) is when x = a.
f”(a) is because f(x) is when x = a.
2. The traffic speed S (mph) on a two-lane road is a function of the traffic density Q (number
of cars per mile) and is given by the formula 290Q^-1 - 0.04Q + 31 for 60 ≤ Q ≤ 400.
Calculate the following:
(dS)/(dQ) =
(d^2S)/(dQ^2) =
3. Find an equation of the tangent line to f(x) = xcos(x) at x = (π)/(4).

Added by Diego J.

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