Calculus Test Questions with Verified Answers Latest Update 2024 (Already Passed)
State the Intermediate Value Theorem - Answers If the function f(x) is continuous on [a,b], and y is a
number between f(a) and f(b), then there exists at least one number x = c in the open interval (a,b) such
that f(c) = y.
State the Chain Rule for Differentiation - Answers n(f(x))^n-1 * f'(x)
What is the integral of ln(x)? - Answers ...
What is the Product Rule? - Answers [f(x) * g'(x)] + [f('x) * g(x)]
Symbolically write the Quotient Rule. - Answers [(f'(x) * g(x)) - ((f(x) * g'(x))] / (g(x))^2
How do you find critical points? - Answers Set f' equal to 0
What does an inflection point signify? - Answers A change in concavity
Does the second derivative need to exist for there to be an inflection point? - Answers No, the second
derivative could be undefined
How do you find a local maximum? - Answers Set the derivative and set it equal to zero (or undefined)
and check it.
How do you find a local minimum? - Answers Set the derivative and set it equal to zero (or undefined)
and check it.
Take the derivative of sin(x). - Answers cos(x)
Take the derivative of cos(x). - Answers -sin(x)
Take the derivative of ln(x). - Answers 1/x
Take the derivative of csc(x). - Answers -csc(x)cot(x)
Take the derivative of arccsc(x). - Answers -u' / |u| √(u^2 - 1)
Take the derivative of arccot(x). - Answers -u' / 1 + u^2
Take the derivative of cot(x). - Answers -csc^2(x)
Take the derivative of sec(x). - Answers sec(x)tan(x)
Take the derivative of arcsec(x). - Answers u' / |u| √(u^2 - 1)
Take the derivative of a^x. - Answers ln(a) * a^x
Take the derivative of log∨a(x). - Answers 1 / ln(a) * x
State the Intermediate Value Theorem - Answers If the function f(x) is continuous on [a,b], and y is a
number between f(a) and f(b), then there exists at least one number x = c in the open interval (a,b) such
that f(c) = y.
State the Chain Rule for Differentiation - Answers n(f(x))^n-1 * f'(x)
What is the integral of ln(x)? - Answers ...
What is the Product Rule? - Answers [f(x) * g'(x)] + [f('x) * g(x)]
Symbolically write the Quotient Rule. - Answers [(f'(x) * g(x)) - ((f(x) * g'(x))] / (g(x))^2
How do you find critical points? - Answers Set f' equal to 0
What does an inflection point signify? - Answers A change in concavity
Does the second derivative need to exist for there to be an inflection point? - Answers No, the second
derivative could be undefined
How do you find a local maximum? - Answers Set the derivative and set it equal to zero (or undefined)
and check it.
How do you find a local minimum? - Answers Set the derivative and set it equal to zero (or undefined)
and check it.
Take the derivative of sin(x). - Answers cos(x)
Take the derivative of cos(x). - Answers -sin(x)
Take the derivative of ln(x). - Answers 1/x
Take the derivative of csc(x). - Answers -csc(x)cot(x)
Take the derivative of arccsc(x). - Answers -u' / |u| √(u^2 - 1)
Take the derivative of arccot(x). - Answers -u' / 1 + u^2
Take the derivative of cot(x). - Answers -csc^2(x)
Take the derivative of sec(x). - Answers sec(x)tan(x)
Take the derivative of arcsec(x). - Answers u' / |u| √(u^2 - 1)
Take the derivative of a^x. - Answers ln(a) * a^x
Take the derivative of log∨a(x). - Answers 1 / ln(a) * x
