MTH 124 Exam 2 questions with
verified answers rated A+
What is a concave up? - correct answer ✔✔ Means that the second derivative is positive
T/F
Concave tells you if something is decreasing or increasing - correct answer ✔✔ F
Steps of determining extrema - correct answer ✔✔ 1. Take the 1st derivative
2. Find critical point(s) of f(x) (f'(x) = 0)
3. Test critical point(s) to determine if it is a max, min, or neither
4. Take the 2nd derivative: Take f''(x) and check concavity of critical point x = c
Steps of determining inflection points - correct answer ✔✔ 1. Take 1st derivative
2. Take 2nd derivative
3. Put critical point(s) into table
4. Write which values are concave up/down, and state your answer as "x = c is a point of
inflection"
On a question about inflection points, if you are asked "where is the rate MAXIMAL?" What
should you do? - correct answer ✔✔ Draw a graph of the point of inflection with a dotted line
split down the middle of it and write on the graph where you can see it switch from concave up
to concave down (or vice versa) to make sure there is an inflection point
What does f">0 mean? - correct answer ✔✔ f'' is concave up (+)
, What does f"<0 mean? - correct answer ✔✔ f'' is concave down (-)
What does f'>0 and f">0 mean? - correct answer ✔✔ f' increasing and f'' is concave up
What does f'>0 and f"<0 mean? - correct answer ✔✔ f'' is increasing and f'' is concave down
T/F
If q"(t)=0 when t=4, then q(t) must have an inflection point at t=4 - correct answer ✔✔ F. You
don't know if it is concave up or concave down
What is the quotient rule equation? - correct answer ✔✔ [f(x)' * g(x) - f(x) * g(x)'] / g(x)^2
What is the derivative of 7^x? - correct answer ✔✔ For any number > 0, take the natural log
multiplied by the original derivative. Ex: ln(a)a^x
What is the derivative of e^x? - correct answer ✔✔ e^x
How do you find the derivative of log base b of x? - correct answer ✔✔ 1 / x ln b
How do you find the derivative of ln x? - correct answer ✔✔ 1 / x
What is a critical point? - correct answer ✔✔ At point x = c, it is called a critical point of f(x)
where f'(c) = 0, if not then it does not exist and there are no critical points
If f'(x) is negative to the LEFT of x = c and positive to the RIGHT, then f has a ________________
at x = c (the critical point(s) you calculated. - correct answer ✔✔ Minimum
verified answers rated A+
What is a concave up? - correct answer ✔✔ Means that the second derivative is positive
T/F
Concave tells you if something is decreasing or increasing - correct answer ✔✔ F
Steps of determining extrema - correct answer ✔✔ 1. Take the 1st derivative
2. Find critical point(s) of f(x) (f'(x) = 0)
3. Test critical point(s) to determine if it is a max, min, or neither
4. Take the 2nd derivative: Take f''(x) and check concavity of critical point x = c
Steps of determining inflection points - correct answer ✔✔ 1. Take 1st derivative
2. Take 2nd derivative
3. Put critical point(s) into table
4. Write which values are concave up/down, and state your answer as "x = c is a point of
inflection"
On a question about inflection points, if you are asked "where is the rate MAXIMAL?" What
should you do? - correct answer ✔✔ Draw a graph of the point of inflection with a dotted line
split down the middle of it and write on the graph where you can see it switch from concave up
to concave down (or vice versa) to make sure there is an inflection point
What does f">0 mean? - correct answer ✔✔ f'' is concave up (+)
, What does f"<0 mean? - correct answer ✔✔ f'' is concave down (-)
What does f'>0 and f">0 mean? - correct answer ✔✔ f' increasing and f'' is concave up
What does f'>0 and f"<0 mean? - correct answer ✔✔ f'' is increasing and f'' is concave down
T/F
If q"(t)=0 when t=4, then q(t) must have an inflection point at t=4 - correct answer ✔✔ F. You
don't know if it is concave up or concave down
What is the quotient rule equation? - correct answer ✔✔ [f(x)' * g(x) - f(x) * g(x)'] / g(x)^2
What is the derivative of 7^x? - correct answer ✔✔ For any number > 0, take the natural log
multiplied by the original derivative. Ex: ln(a)a^x
What is the derivative of e^x? - correct answer ✔✔ e^x
How do you find the derivative of log base b of x? - correct answer ✔✔ 1 / x ln b
How do you find the derivative of ln x? - correct answer ✔✔ 1 / x
What is a critical point? - correct answer ✔✔ At point x = c, it is called a critical point of f(x)
where f'(c) = 0, if not then it does not exist and there are no critical points
If f'(x) is negative to the LEFT of x = c and positive to the RIGHT, then f has a ________________
at x = c (the critical point(s) you calculated. - correct answer ✔✔ Minimum
