Math 142 Exam 2 Questions with
complete solution 2026
Which of the following is a step/label we discussed in class for the concavity test?
a. partition numbers of f"
b. sign chart of f'
c. critical values of f(x)
d. partition numbers of f'
e. critical values of f" - correct answer ✔a
To find vertical asymptotes of a rational fun, we do which of the following
a. find left and right limits as x -> 0
b. factor the numerator and denominator, cancel common factors, then look for where we get a zero in
the denominator
c. factor the numerator and denominator, then look for factors that cancel out completely
d. find the limit as x approaches positive and negative infinity
e. none of the above - correct answer ✔b
f'(x) of logBASE4(e^3x) - correct answer ✔3/ln(x)
to find any horizontal asymptotes of (3x^2 +4x^5-x)/(x^3 +x^4 -2x^2), we divide eery term by which of
the following
a. x^3
b. x
c. x^2
d. x^4
, e. x^5 - correct answer ✔d
If f(x) is continuous on its domain (-inf, inf), f'(3) = 0 and f'(3) = 0, we can conclude
I. x=3 is a critical value of f(X)
II. f(X) has an inflection point at x=3
III. f(x) does not have any local extrema at x=3
a. I only
b. I and III
c. I and II
d. II
e. I, II, and II - correct answer ✔a
Which on of the following is NOT part of the work in step 3 of the optimization process?
a. finding the derivative of the fxn
b. finding the appropriate interval for the fxn
c. using the appropriate test to find where the abs min/max occurs
d. finding the critical values of the fxn
e. none of the above (all are in step 3) - correct answer ✔b
given g"(x)= [(x-5)(x+6)]/(x+8)^7, how many partition #s of g"(x) are there?
a. 4
b. 2
c. 7
d. 1
complete solution 2026
Which of the following is a step/label we discussed in class for the concavity test?
a. partition numbers of f"
b. sign chart of f'
c. critical values of f(x)
d. partition numbers of f'
e. critical values of f" - correct answer ✔a
To find vertical asymptotes of a rational fun, we do which of the following
a. find left and right limits as x -> 0
b. factor the numerator and denominator, cancel common factors, then look for where we get a zero in
the denominator
c. factor the numerator and denominator, then look for factors that cancel out completely
d. find the limit as x approaches positive and negative infinity
e. none of the above - correct answer ✔b
f'(x) of logBASE4(e^3x) - correct answer ✔3/ln(x)
to find any horizontal asymptotes of (3x^2 +4x^5-x)/(x^3 +x^4 -2x^2), we divide eery term by which of
the following
a. x^3
b. x
c. x^2
d. x^4
, e. x^5 - correct answer ✔d
If f(x) is continuous on its domain (-inf, inf), f'(3) = 0 and f'(3) = 0, we can conclude
I. x=3 is a critical value of f(X)
II. f(X) has an inflection point at x=3
III. f(x) does not have any local extrema at x=3
a. I only
b. I and III
c. I and II
d. II
e. I, II, and II - correct answer ✔a
Which on of the following is NOT part of the work in step 3 of the optimization process?
a. finding the derivative of the fxn
b. finding the appropriate interval for the fxn
c. using the appropriate test to find where the abs min/max occurs
d. finding the critical values of the fxn
e. none of the above (all are in step 3) - correct answer ✔b
given g"(x)= [(x-5)(x+6)]/(x+8)^7, how many partition #s of g"(x) are there?
a. 4
b. 2
c. 7
d. 1
