Exam 3: The Derivative

A pump is used to empty a 350-gallon hot tub. The table shows the amount of water, W(t), measured in gallons, remaining in the hot tub at time t, measured in minutes after the pump is turned on. T 0 15 30 45 60 90 W(t) 350 320 280 225 170 105 Approximate W'(30) in this context.

Let $f(x)=\lfloor x\rfloor$ Which of the following is true?

Let $f ( x ) = \frac { 5 } { \pi }$ Then $f ^ { \prime } ( x )$ is

Let $f ( x ) = \frac { x ^ { 2 } + x } { x }$ Assuming $x \neq 0 , f ^ { \prime } ( x )$ is

An equation of the tangent line to the graph $f ( x ) = \sqrt { x + 3 }$ at the point (6, 3) is

The derivative of $f ( x ) = - 8 x + 7$ at x = 0 is

The fourth derivative $\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 2 } - e ^ { x } \right)$ is

Let $f ( x ) = | x |$ Which of the following is true?

Let $f ( x ) = - 3 ( x + 5 ) ^ { 2 }$ . Then $f ^ { \prime } ( x )$ is

Let $f ( x ) = e ^ { 2 } x ^ { 3 }$ Then $f ^ { \prime } ( x )$ is

An equation of the tangent line to the graph $f ( x ) = 2 x - x ^ { 2 }$ at the point (-1,-3) is

Let $f ( x ) = x - e ^ { x }$ . Then $f ^ { \prime } ( x ) < 0$ for all x in

Let $f ( x ) = \sqrt [ 3 ] { x }$ Which of the following is true?

Let $f ( x ) = \frac { 3 } { \sqrt { x } } + 4$ Then $f ^ { \prime } ( x )$ is

Let $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 3 x + 4$ Then $f ^ { \prime } ( x ) = 0$ if x is

Let $y = 3 \sin x + 2 \cos x$ Then $y\prime\prime$ is

An equation of the tangent line to the graph $f ( x ) = x ^ { 2 } - x$ at the point (-2, 6) is

Let y = x cos x. Then $y\prime\prime$ is

The instantaneous rate of change of $f ( x ) = 3 x - 2 x ^ { 2 }$ at c = 2 is

Let $f ( x ) = \frac { 1 } { e }$ Then $f ^ { \prime } ( x )$ is