Question 1

Let $f ( x ) = 4 e ^ { x } + 3 x$ Then which of the following is the largest interval, of those listed, for which for all x in that interval?

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \ln \frac { 3 } { 4 } \right)$ 
C)  $\left( - \ln \frac { 3 } { 4 } , \ln \frac { 3 } { 4 } \right)$ 
D)  $\left( - \infty , \ln \frac { 3 } { 4 } \right)$ 
E)  $\varnothing$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \ln \frac { 3 } { 4 } \right)$ 
C)  $\left( - \ln \frac { 3 } { 4 } , \ln \frac { 3 } { 4 } \right)$ 
D)  $\left( - \infty , \ln \frac { 3 } { 4 } \right)$ 
E)  $\varnothing$

Question 2

The derivative of $f ( x ) = \frac { 4 } { x } + 5$ at x = -2 is

Accepted Answer

A) -4 
B) -2 
C) -1 
D) 2 
E) 4 
A) -4 
B) -2 
C) -1 
D) 2 
E) 4

Question 3

Let $f ( x ) = \frac { 4 x } { 3 x + 5 }$ Then $f ^ { \prime } ( x )$ is

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 20 } { 3 x + 5 }$ 
C)  $- \frac { 20 } { ( 3 x + 5 ) ^ { 2 } }$ 
D)  $\frac { 20 } { ( 3 x + 5 ) ^ { 2 } }$ 
E)  $\frac { 24 x - 5 } { ( 3 x + 5 ) ^ { 2 } }$ 
A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 20 } { 3 x + 5 }$ 
C)  $- \frac { 20 } { ( 3 x + 5 ) ^ { 2 } }$ 
D)  $\frac { 20 } { ( 3 x + 5 ) ^ { 2 } }$ 
E)  $\frac { 24 x - 5 } { ( 3 x + 5 ) ^ { 2 } }$

Question 4

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

Accepted Answer

A)  $\csc x \cot x + \sec x \tan x$ 
B)  $\csc x \cot x - \sec x \tan x$ 
C)  $- \csc x \cot x + \sec x \tan x$ 
D)  $- \csc x \cot x - \sec x \tan x$ 
E)  $\csc x \tan x - \sec x \cot x$ 
A)  $\csc x \cot x + \sec x \tan x$ 
B)  $\csc x \cot x - \sec x \tan x$ 
C)  $- \csc x \cot x + \sec x \tan x$ 
D)  $- \csc x \cot x - \sec x \tan x$ 
E)  $\csc x \tan x - \sec x \cot x$

Let $f ( x ) = 4 e ^ { x } + 3 x$ Then which of the following is the largest interval, of those listed, for which for all x in that interval?

The derivative of $f ( x ) = \frac { 4 } { x } + 5$ at x = -2 is

Let $f ( x ) = \frac { 4 x } { 3 x + 5 }$ Then $f ^ { \prime } ( x )$ is

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

Preparing for Calculus

Limits and Continuity

More About Derivatives

Applications of the Derivative

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Exam 3: The Derivative

Let f(x)=4ex+3xf ( x ) = 4 e ^ { x } + 3 xf(x)=4ex+3x Then which of the following is the largest interval, of those listed, for which for all x in that interval?

The derivative of f(x)=4x+5f ( x ) = \frac { 4 } { x } + 5f(x)=x4​+5 at x = -2 is

Let f(x)=4x3x+5f ( x ) = \frac { 4 x } { 3 x + 5 }f(x)=3x+54x​ Then f′(x)f ^ { \prime } ( x )f′(x) is

Let f(x)=1−tan⁡xsin⁡xf ( x ) = \frac { 1 - \tan x } { \sin x }f(x)=sinx1−tanx​ Then f′(x)f ^ { \prime } ( x )f′(x) is

Preparing for Calculus

Limits and Continuity

More About Derivatives

Applications of the Derivative

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Let $f ( x ) = 4 e ^ { x } + 3 x$ Then which of the following is the largest interval, of those listed, for which for all x in that interval?

The derivative of $f ( x ) = \frac { 4 } { x } + 5$ at x = -2 is

Let $f ( x ) = \frac { 4 x } { 3 x + 5 }$ Then $f ^ { \prime } ( x )$ is

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