FiltersDone

Question type

Essay

Multiple Choice

Short Answer

True False

Matching

Exam 2: Differentiation: Basic Concepts

Show Answer

Share

---

All types

Filters

Study Flashcards

Question 71

Short Answer

Review LaterAdd Note

Review Later

If f (x) represents the price per barrel of oil in terms of time, what does $\frac { f \left( x _ { 0 } + h \right) - f \left( x _ { 0 } \right) } { h }$ represent? What about $\lim _ { h \rightarrow 0 } \frac { f \left( x _ { 0 } + h \right) - f \left( x _ { 0 } \right) } { h }$ ?

Correct Answer

verified

The average rate of change of ...

View Answer

Show Answer

Question 72

Multiple Choice

Review LaterAdd Note

Review Later

Differentiate: $f ( x ) = x ^ { 4 } + 7$

A) $4 x ^ { 3 }$
B) $4 x ^ { 3 } + 7$
C) $4 x ^ { 5 } + 7 x$
D) $3 x ^ { 3 }$

E) A) and B)
F) B) and C)

Correct Answer

verified

Show Answer

Question 73

Short Answer

Review LaterAdd Note

An equation for the tangent line to the curve $y = \left( 6 x ^ { 2 } + x - 1 \right) ^ { 3 }$ at the point where x = 0 is

Find the equation of the tangent to the graph of $f ( x ) = x ^ { 2 } - 9 x + 16$ at the point (1, 8).

Find an equation for the tangent line to the curve $x ^ { 2 } + y ^ { 3 } = x y + 1$ at the point (1, -1).

Find all points on the graph of the function $f ( x ) = x ^ { 3 } ( 5 x + 20 )$ where the tangent line is horizontal.

Find $\frac { d y } { d x }$ , where $\sqrt { x } + \sqrt { y } = x y$ .

What is the rate of change of $f ( t ) = \frac { 7 t - 4 } { t + 3 }$ with respect to t when t = 3?

Find the equation of the line that is tangent to the curve $f ( x ) = 5 + 2 x ^ { 2 } - x ^ { 3 }$ at the point (1, 6).

Differentiate: $f ( x ) = \frac { 2 } { 3 } x ^ { 6 } - \frac { 7 } { 3 } x + \frac { 8 } { 7 x } - \sqrt [ 6 ] { x }$

If $x ^ { 2 } + 2 y ^ { 2 } = 5$ , then $\frac { d y } { d x } = 2 x$ .

An efficiency study at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have produced $Q ( t ) = - t ^ { 3 } + 6 t ^ { 2 } + 18 t$ units t hours later. At what rate, in units/hour, is the worker's rate of production changing with respect to time at 9:00 A.M.?

Find the equation of the tangent line to the curve $f ( x ) = x ^ { 3 } - x ^ { 2 } + 7$ at the point (1, 7).

Differentiate: $f ( x ) = \frac { 2 } { 3 } x ^ { 6 } - \frac { 5 x } { 6 } + \frac { 2 } { 3 x } - \sqrt [ 5 ] { x }$

Find $\frac { d y } { d x }$ , where $x y ^ { 3 } - 3 x ^ { 2 } = 7 y$ .

Find an equation for the tangent line to the curve $y = \left( 7 x ^ { 2 } + x - 1 \right) ^ { 3 }$ at the point where x = 0.

The equation of the line tangent to the graph of $f ( x ) = 3 \sqrt { x }$ at x = 1 is

For $f ( x ) = - \frac { 3 } { \sqrt { x } }$ , find the average rate of change of f (x) with respect to x as x changes from 144 to 145. Then use calculus to find the instantaneous rate of change at x = 144. Round your answer to six decimal places, if necessary.

If f (x) represents the price per barrel of oil in terms of time, what does $\frac { f \left( x _ { 0 } + h \right) - f \left( x _ { 0 } \right) } { h }$ represent? What about $\lim _ { h \rightarrow 0 } \frac { f \left( x _ { 0 } + h \right) - f \left( x _ { 0 } \right) } { h }$ ?

The equation of the line tangent to the graph of $f ( x ) = x ^ { 2 } + 3 x$ at x = 2 is