What does it mean for a function to have a horizontal tangent line?
MA Chapter 5 Review

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A function has a horizontal tangent line at a point if the derivative at that point is zero, indicating that the slope of the tangent line is flat.
2.
FLASHCARD QUESTION
Front
What is the Mean Value Theorem?
Back
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).
3.
FLASHCARD QUESTION
Front
What does it indicate if the first derivative of a function is negative at a point?
Back
If the first derivative f'(x) is negative at a point, it indicates that the function f(x) is decreasing at that point.
4.
FLASHCARD QUESTION
Front
How do you find critical points of a function?
Back
Critical points occur where the first derivative f'(x) is zero or undefined. To find them, set f'(x) = 0 and solve for x.
5.
FLASHCARD QUESTION
Front
What is the significance of critical points in calculus?
Back
Critical points are important because they can indicate local maxima, local minima, or points of inflection in the graph of a function.
6.
FLASHCARD QUESTION
Front
What does it mean if f'(x) < 0 on an interval?
Back
If f'(x) < 0 on an interval, it means that the function f(x) is decreasing throughout that interval.
7.
FLASHCARD QUESTION
Front
What is a zero of a function?
Back
A zero of a function is a value of x for which f(x) = 0. It represents the x-intercepts of the graph of the function.
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