Calculus Finals Review (MC) Fall 2024

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•
Mathematics
•
12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the derivative of the function f(x) = (x - 1)(x + 2)?
Back
f'(x) = (x - 1)'(x + 2) + (x - 1)(x + 2)' = 1(x + 2) + (x - 1)(1) = 2x + 1. To find f'(0), plug in 0: f'(0) = 1.
2.
FLASHCARD QUESTION
Front
How do you find the speed of an object given its distance function s(t) = t^3 - 6t^2 - 4 when acceleration is 0?
Back
First, find the acceleration by taking the second derivative of s(t). Set the acceleration to 0 and solve for t. Then, plug that t value into s'(t) to find the speed.
3.
FLASHCARD QUESTION
Front
What does it mean for the slope of the tangent line to be positive?
Back
The slope of the tangent line is positive when the function is increasing at that point. This occurs when the derivative of the function is greater than 0.
4.
FLASHCARD QUESTION
Front
What is the limit of a function as x approaches a certain value?
Back
The limit is the value that a function approaches as the input approaches a certain value. For example, lim (x -> 1) of f(x) = 4 means as x gets closer to 1, f(x) approaches 4.
5.
FLASHCARD QUESTION
Front
Back
6.
FLASHCARD QUESTION
Front
What is the Product Rule in calculus?
Back
The Product Rule states that if you have two functions u(x) and v(x), then the derivative of their product is: (uv)' = u'v + uv'.
7.
FLASHCARD QUESTION
Front
Define acceleration in terms of calculus.
Back
Acceleration is the second derivative of the position function with respect to time, or the derivative of velocity.
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