Question 1

Determine the equation of the tangent line at x=0 and the value of f(x)at x=1.5 given $f(x)=a^{x}$ for all values of a

Accepted Answer

A) y=(ln a)x+1, y=1.5(ln a)+1 
B) y=(ln a)(a1.5)x-1, y=-1 
C) y=(a1.5)[(ln a)x-1], y=-1 
D) y=(ln a)x-1, y=1.5(ln a)-1 
E) y=(ln a)x-1, y=1.5 
A) y=(ln a)x+1, y=1.5(ln a)+1 
B) y=(ln a)(a1.5)x-1, y=-1 
C) y=(a1.5)[(ln a)x-1], y=-1 
D) y=(ln a)x-1, y=1.5(ln a)-1 
E) y=(ln a)x-1, y=1.5

Question 2

Sketch a graph of a function whose $f^{\prime}(x)=0$ at x=-1, $f^{\prime}(x)$  -1,

Accepted Answer

The answer of Sketch a graph of a function whose...

Question 3

A normal distribution in statistics is modeled by the function $N(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2}$ determine where the maximum value of the function would occur.

Accepted Answer

A) -2 
B) -1 
C) 0 
D) -2 $\pi$ 
E)  $\ell$ -2 
A) -2 
B) -1 
C) 0 
D) -2 $\pi$ 
E)  $\ell$ -2

Question 4

The cost C(q)(in dollars)of producing a quantity q of a certain product is shown in the graph below.The average cost is given by $a(q)=\frac{C(q)}{q}$ .Graphically, a(q)is the slope of the line between which two points?

Accepted Answer

A) (0, 0) 
B)  $(q, C(q))$ 
C) (0, q) 
D)  $(0, C(q))$ 
A) (0, 0) 
B)  $(q, C(q))$ 
C) (0, q) 
D)  $(0, C(q))$

Question 5

Below is the graph of the derivative of a function f, i.e., it is a graph of y = f '(x).Is f increasing or decreasing on the interval $2 \leq x \leq 3$ ?

Accepted Answer

The answer of Below is the graph of the derivative...

Question 6

Consider the one-parameter family of functions given by $e^{A x}+e^{-A x}$ for $A>0$ .What are the effects on the graph as the value of A is decreased?

Accepted Answer

A) The global minimum is decreased. 
B) The global minimum is increased. 
C) The curvature is decreased (i.e.the curve is wider) 
D) The curvature is increased (i.e.the curve is narrower) 
A) The global minimum is decreased. 
B) The global minimum is increased. 
C) The curvature is decreased (i.e.the curve is wider) 
D) The curvature is increased (i.e.the curve is narrower)

Question 7

Below is the graph of the rate r at which people arrive for lunch at Cafeteria Charlotte.Checkers start at 12:00 noon and can pass people through at a constant rate of 5 people/minute.Let f(t)be the length of the line (i.e.the number of people)at time t.Suppose that at 11:50 there are already 150 people lined up.Using the graph together with this information, is f concave up or down on the interval 11:55 < t < 12:07?

Accepted Answer

The answer of Below is the graph of the rate...

Question 8

Determine the $\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x+a}$ , given a=-1

Accepted Answer

The answer of Determine the $\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x+a}$...

Determine the equation of the tangent line at x=0 and the value of f(x)at x=1.5 given $f(x)=a^{x}$ for all values of a

Sketch a graph of a function whose $f^{\prime}(x)=0$ at x=-1, $f^{\prime}(x)$ < 0 when x< -1, $f^{\prime}(x)$ < 0 when x> -1,

A normal distribution in statistics is modeled by the function $N(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2}$ determine where the maximum value of the function would occur.

Consider the one-parameter family of functions given by $e^{A x}+e^{-A x}$ for $A>0$ .What are the effects on the graph as the value of A is decreased?

Determine the $\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x+a}$ , given a=-1

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Exam 4: Using the Derivative

Determine the equation of the tangent line at x=0 and the value of f(x)at x=1.5 given f(x)=axf(x)=a^{x}f(x)=ax for all values of a

Sketch a graph of a function whose f′(x)=0f^{\prime}(x)=0f′(x)=0 at x=-1, f′(x)f^{\prime}(x)f′(x) < 0 when x< -1, f′(x)f^{\prime}(x)f′(x) < 0 when x> -1,

A normal distribution in statistics is modeled by the function N(x)=12πe−x2/2N(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2}N(x)=2π​1​e−x2/2 determine where the maximum value of the function would occur.

The cost C(q)(in dollars)of producing a quantity q of a certain product is shown in the graph below.The average cost is given by a(q)=C(q)qa(q)=\frac{C(q)}{q}a(q)=qC(q)​ .Graphically, a(q)is the slope of the line between which two points?

Below is the graph of the derivative of a function f, i.e., it is a graph of y = f '(x).Is f increasing or decreasing on the interval 2≤x≤32 \leq x \leq 32≤x≤3 ?

Consider the one-parameter family of functions given by eAx+e−Axe^{A x}+e^{-A x}eAx+e−Ax for A>0A>0A>0 .What are the effects on the graph as the value of A is decreased?

Determine the lim⁡x→ax2−a2x+a\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x+a}limx→a​x+ax2−a2​ , given a=-1

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Determine the equation of the tangent line at x=0 and the value of f(x)at x=1.5 given $f(x)=a^{x}$ for all values of a

Sketch a graph of a function whose $f^{\prime}(x)=0$ at x=-1, $f^{\prime}(x)$ < 0 when x< -1, $f^{\prime}(x)$ < 0 when x> -1,

A normal distribution in statistics is modeled by the function $N(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2}$ determine where the maximum value of the function would occur.

Consider the one-parameter family of functions given by $e^{A x}+e^{-A x}$ for $A>0$ .What are the effects on the graph as the value of A is decreased?

Determine the $\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x+a}$ , given a=-1