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Calculus vocabulary Exam Questions with Verified Answers Latest Update (Graded A+)
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Calculus vocabulary Exam Questions with Verified Answers Latest Update (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 vertica...

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  • November 14, 2024
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  • 2024/2025
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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

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