Solution Manual for Calculus for Business, Economics,
and the Social and Life Sciences, Brief Version, 11th
Edition By Hoffmann
(unit 1 review) - ANSWER: (exam 1 review)
How solve rational inequality? - ANSWER: 1. find x values
2. insert new x values into the equation to see if it satisfy the statement
How to evaluate piecewise function with limits? - ANSWER: 1. look at the limit x→#
f(x)
2. choose which interval that satisfy the limit
3. insert # into the equation to find the value.
How to compute the limit? - ANSWER: 1. Simplify by factoring
2. Cancel any match numerator and denominator
3. Insert the x value into equation
Intermediate Value Theorem - ANSWER: If f is continuous on [a,b] and k is a number
between f(a) and f(b), then there exists at least one number c such that f(c)=k
On which of the following intervals does the intermediate value theorem guarantee
that f(x) has a zero? Select all correct answers. f(x)=3x2−2x−2 - ANSWER: (0,2)
1. Insert x values (from an interval) into the equation
2. if they have opposite y value signs, then it guarantees it.
what is the instantaneous rate of change formula - ANSWER: f(x+h)-f(x) /h.
think it as like a slope formula but you have extra step to figure out y values
Find the average rate of change of the function f(x), given below, from x=−3 to x=t.
f(x)=−4x2−4x−2 - ANSWER: 1. insert x values into f(x)
2. for the numerator, f(t)-f(-3)
3. for the denominator, it is t-(-3)
Given the function f(x)=x2−2x, which of the following is the correct limit definition of
f′(2)? - ANSWER: 1. follow the instantaneous rate of change formula
2. put (x+h) into every x inside the f(x) equation. [x^2-2x is ((x+h)^2−2(x+h))]
3. put (x) into every x inside the f(x) equation.
4. simplify
how to compute derivatives of exponent functions? - ANSWER: 7^xln7
, What is r′(x) when r(x)=ln (x÷ 4x^2+x) - ANSWER: 1. Using the division in the
properties of logarithms in derivative.
2. split the x and 4x^2+x
3. which is lnx-ln(4x^2+x)
4. turn them into derivatives
Find the derivative of the following: 𝑔(𝑥)=(3+5𝑥)/x^4 - ANSWER: 1. Identify f(x) and
g(x)
2. Convert into derivative
3. Follow the quotient derivative rule
4. Split up the term
5. Simplify by canceling
lim𝑥→∞ x+3 =-5/4 What does this tell you about the graph of y=f(x)=x+3 - ANSWER:
f(x) has a horizontal asymptote at y=-5/4.
Find the vertical asymptote(s) of R(x) = (x−3)(x+5) / (x^2+9)(x+4) - ANSWER: x=-4
It can be found the by the denominator x=a. Not the hole (cancels)
Which of the following are correct interpretations of what the derivative of a
function represents at a point? - ANSWER: The instantaneous rate of change of the
function at the point. The slope of the tangent line to the graph of the function at
the point.
What is the derivative of exponential function - ANSWER: f'(x) times e^f(x)
Use any method to find the derivative of the following: 𝑓(𝑥)=5𝑥−𝑒^3𝑥^2 -
ANSWER: 1. logarithimic function rule
2. the exponential function rule
ln (5)(5^x)-6xe^3x^2
What is Derivative rules for logarithmic functions of any base (log. Not lnx) -
ANSWER: 1 / x ln (a)
(unit 2 review) - ANSWER: (exam 2 review)
what is the quotient rule in derivative - ANSWER: it's different from Product rule. g(x)
goes first
how to find derivative of h(x)=1 / (2x2+2x+1)^5 - ANSWER: First, using negative
exponent rules, rewrite h(x)=1 / (2x2+2x+1)^5 as (2x2+2x+1)^−5
Calculate the value of C(x) when the marginal cost is 760. C(x)= 20,000+980x−x^2 for
0≤x<1,000. - ANSWER: 1. find derivative of C(x)
2. 760=980-2x
2. bring the 760 to the other side
and the Social and Life Sciences, Brief Version, 11th
Edition By Hoffmann
(unit 1 review) - ANSWER: (exam 1 review)
How solve rational inequality? - ANSWER: 1. find x values
2. insert new x values into the equation to see if it satisfy the statement
How to evaluate piecewise function with limits? - ANSWER: 1. look at the limit x→#
f(x)
2. choose which interval that satisfy the limit
3. insert # into the equation to find the value.
How to compute the limit? - ANSWER: 1. Simplify by factoring
2. Cancel any match numerator and denominator
3. Insert the x value into equation
Intermediate Value Theorem - ANSWER: If f is continuous on [a,b] and k is a number
between f(a) and f(b), then there exists at least one number c such that f(c)=k
On which of the following intervals does the intermediate value theorem guarantee
that f(x) has a zero? Select all correct answers. f(x)=3x2−2x−2 - ANSWER: (0,2)
1. Insert x values (from an interval) into the equation
2. if they have opposite y value signs, then it guarantees it.
what is the instantaneous rate of change formula - ANSWER: f(x+h)-f(x) /h.
think it as like a slope formula but you have extra step to figure out y values
Find the average rate of change of the function f(x), given below, from x=−3 to x=t.
f(x)=−4x2−4x−2 - ANSWER: 1. insert x values into f(x)
2. for the numerator, f(t)-f(-3)
3. for the denominator, it is t-(-3)
Given the function f(x)=x2−2x, which of the following is the correct limit definition of
f′(2)? - ANSWER: 1. follow the instantaneous rate of change formula
2. put (x+h) into every x inside the f(x) equation. [x^2-2x is ((x+h)^2−2(x+h))]
3. put (x) into every x inside the f(x) equation.
4. simplify
how to compute derivatives of exponent functions? - ANSWER: 7^xln7
, What is r′(x) when r(x)=ln (x÷ 4x^2+x) - ANSWER: 1. Using the division in the
properties of logarithms in derivative.
2. split the x and 4x^2+x
3. which is lnx-ln(4x^2+x)
4. turn them into derivatives
Find the derivative of the following: 𝑔(𝑥)=(3+5𝑥)/x^4 - ANSWER: 1. Identify f(x) and
g(x)
2. Convert into derivative
3. Follow the quotient derivative rule
4. Split up the term
5. Simplify by canceling
lim𝑥→∞ x+3 =-5/4 What does this tell you about the graph of y=f(x)=x+3 - ANSWER:
f(x) has a horizontal asymptote at y=-5/4.
Find the vertical asymptote(s) of R(x) = (x−3)(x+5) / (x^2+9)(x+4) - ANSWER: x=-4
It can be found the by the denominator x=a. Not the hole (cancels)
Which of the following are correct interpretations of what the derivative of a
function represents at a point? - ANSWER: The instantaneous rate of change of the
function at the point. The slope of the tangent line to the graph of the function at
the point.
What is the derivative of exponential function - ANSWER: f'(x) times e^f(x)
Use any method to find the derivative of the following: 𝑓(𝑥)=5𝑥−𝑒^3𝑥^2 -
ANSWER: 1. logarithimic function rule
2. the exponential function rule
ln (5)(5^x)-6xe^3x^2
What is Derivative rules for logarithmic functions of any base (log. Not lnx) -
ANSWER: 1 / x ln (a)
(unit 2 review) - ANSWER: (exam 2 review)
what is the quotient rule in derivative - ANSWER: it's different from Product rule. g(x)
goes first
how to find derivative of h(x)=1 / (2x2+2x+1)^5 - ANSWER: First, using negative
exponent rules, rewrite h(x)=1 / (2x2+2x+1)^5 as (2x2+2x+1)^−5
Calculate the value of C(x) when the marginal cost is 760. C(x)= 20,000+980x−x^2 for
0≤x<1,000. - ANSWER: 1. find derivative of C(x)
2. 760=980-2x
2. bring the 760 to the other side
