Calculus vocabulary Exam Questions with Verified Answers Latest Update 2024-2025 (Graded A+)
Continuous at x = a - Answers limit of f(x) as x->a = f(a)
Differentiable - Answers The derivative exists.
Reasons for a function to not be differentiable - Answers not continuous
cusp/sharp corner
vertical tangent
Intermediate Value Theorem - Answers If f(x) is continuous on [a, b], then it must hit all y-values
between f(a) and f(b).
Mean Value Theorem - Answers If f(x) is continuous on [a, b] and differentiable on (a, b), then there
must be a point c in the open interval where f'(c) = (f(b) - f(a))/(b-a)
Extreme Value Theorem - Answers If f(x) is continuous on [a, b], then it has an absolute max and
absolute min on the interval
First Derivative Test - Answers Check for local extrema by using a number line for f'
Second derivative test - Answers Check for local extrema by checking the concavity at critical points
Closed interval method - Answers Check for absolute extrema on a closed interval by checking the y-
values at the end points and critical points in the interval
Chain rule - Answers Allows you to take the derivative of a composite function.
Implicit differentiation - Answers Allows you to take the derivative of a relation that is not solved for y.
Average rate of change on an interval - Answers (f(b) - f(a))/(b - a)
Definition of derivative of function at a point. - Answers lim as x-> a of (f(x) - f(a))/(x - a)
Definition of derivative of function as a function - Answers lim as h->0 of (f(x+h) - f(h))/h
Riemann sum - Answers Approximate a definite integral using rectangles
Trapezoidal rule - Answers Approximate a definite integral using trapezoids
Definite integral - Answers Finds net area under curve
Velocity - Answers Rate of change of position function
Acceleration - Answers Rate of change of velocity function
Continuous at x = a - Answers limit of f(x) as x->a = f(a)
Differentiable - Answers The derivative exists.
Reasons for a function to not be differentiable - Answers not continuous
cusp/sharp corner
vertical tangent
Intermediate Value Theorem - Answers If f(x) is continuous on [a, b], then it must hit all y-values
between f(a) and f(b).
Mean Value Theorem - Answers If f(x) is continuous on [a, b] and differentiable on (a, b), then there
must be a point c in the open interval where f'(c) = (f(b) - f(a))/(b-a)
Extreme Value Theorem - Answers If f(x) is continuous on [a, b], then it has an absolute max and
absolute min on the interval
First Derivative Test - Answers Check for local extrema by using a number line for f'
Second derivative test - Answers Check for local extrema by checking the concavity at critical points
Closed interval method - Answers Check for absolute extrema on a closed interval by checking the y-
values at the end points and critical points in the interval
Chain rule - Answers Allows you to take the derivative of a composite function.
Implicit differentiation - Answers Allows you to take the derivative of a relation that is not solved for y.
Average rate of change on an interval - Answers (f(b) - f(a))/(b - a)
Definition of derivative of function at a point. - Answers lim as x-> a of (f(x) - f(a))/(x - a)
Definition of derivative of function as a function - Answers lim as h->0 of (f(x+h) - f(h))/h
Riemann sum - Answers Approximate a definite integral using rectangles
Trapezoidal rule - Answers Approximate a definite integral using trapezoids
Definite integral - Answers Finds net area under curve
Velocity - Answers Rate of change of position function
Acceleration - Answers Rate of change of velocity function
