Question 1

Find all relative extrema of the function $f ( x ) = \frac { 4 } { x ^ { 2 } + 2 }$ . Use the Second-Derivative Test when applicable.

Accepted Answer

A) The relative maximum is $( 2,0 )$ . 
B) The relative minimum is $( 0,2 )$ . 
C) The relative maximum is $( 0,2 )$ . 
D) The relative minimum is $( 0,2 )$ . 
E) The relative maximum is $( 4,0 )$ . 
A) The relative maximum is $( 2,0 )$ . 
B) The relative minimum is $( 0,2 )$ . 
C) The relative maximum is $( 0,2 )$ . 
D) The relative minimum is $( 0,2 )$ . 
E) The relative maximum is $( 4,0 )$ .

Question 2

For the given function, find the relative minima. $y = x ^ { 3 } - 9 x ^ { 2 } - 48 x + 10$

Accepted Answer

A)  $( - 2,62 )$ 
B)  $( 8 , - 438 )$ 
C)  $( - 2 , - 114 )$ 
D)  $( - 8 , - 694 )$ 
E) no relative minima 
A)  $( - 2,62 )$ 
B)  $( 8 , - 438 )$ 
C)  $( - 2 , - 114 )$ 
D)  $( - 8 , - 694 )$ 
E) no relative minima

Question 3

Use the graph of $y = f ( x )$ to identify at which of the indicated points the derivative $f ^ { \prime } ( x )$ changes from negative to positive.

Accepted Answer

A) (2,4), (5,6) 
B) (-1,2) 
C) (2,4) 
D) (-1,2), (2,4) 
E) (-1,2), (5,6) 
A) (2,4), (5,6) 
B) (-1,2) 
C) (2,4) 
D) (-1,2), (2,4) 
E) (-1,2), (5,6)

Find all relative extrema of the function $f ( x ) = \frac { 4 } { x ^ { 2 } + 2 }$ . Use the Second-Derivative Test when applicable.

For the given function, find the relative minima. $y = x ^ { 3 } - 9 x ^ { 2 } - 48 x + 10$

Use the graph of $y = f ( x )$ to identify at which of the indicated points the derivative $f ^ { \prime } ( x )$ changes from negative to positive. $Use the graph of y = f ( x ) to identify at which of the indicated points the derivative f ^ { \prime } ( x ) changes from negative to positive.$

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Exam 9: Applications of the Derivative

Find all relative extrema of the function f(x)=4x2+2f ( x ) = \frac { 4 } { x ^ { 2 } + 2 }f(x)=x2+24​ . Use the Second-Derivative Test when applicable.

For the given function, find the relative minima. y=x3−9x2−48x+10y = x ^ { 3 } - 9 x ^ { 2 } - 48 x + 10y=x3−9x2−48x+10

Use the graph of y=f(x)y = f ( x )y=f(x) to identify at which of the indicated points the derivative f′(x)f ^ { \prime } ( x )f′(x) changes from negative to positive.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Find all relative extrema of the function $f ( x ) = \frac { 4 } { x ^ { 2 } + 2 }$ . Use the Second-Derivative Test when applicable.

For the given function, find the relative minima. $y = x ^ { 3 } - 9 x ^ { 2 } - 48 x + 10$

Use the graph of $y = f ( x )$ to identify at which of the indicated points the derivative $f ^ { \prime } ( x )$ changes from negative to positive. $Use the graph of y = f ( x ) to identify at which of the indicated points the derivative f ^ { \prime } ( x ) changes from negative to positive.$