Derivative Review
Flashcard
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What does it mean for a function to be continuous but not differentiable?
Back
A function is continuous at a point if there are no breaks, jumps, or holes in the graph at that point. However, it may not be differentiable if it has a sharp corner or cusp at that point.
2.
FLASHCARD QUESTION
Front
How do you find the equation of the tangent line to a function at a given point?
Back
To find the equation of the tangent line, first calculate the derivative of the function to find the slope at the given point. Then use the point-slope form of the line: y - y1 = m(x - x1), where (x1, y1) is the point on the curve.
3.
FLASHCARD QUESTION
Front
What is implicit differentiation?
Back
Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y, without solving for y explicitly.
4.
FLASHCARD QUESTION
Front
What does the derivative of a function represent?
Back
The derivative represents the slope of the tangent line to the graph of the function at a given point, indicating the rate of change of the function with respect to its variable.
5.
FLASHCARD QUESTION
Front
Find the derivative of y = 2x^2(3x - 4).
Back
The derivative is 18x^2 - 16x.
6.
FLASHCARD QUESTION
Front
What is the power rule for differentiation?
Back
The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1), where n is a real number.
7.
FLASHCARD QUESTION
Front
What is the product rule for differentiation?
Back
The product rule states that if u(x) and v(x) are two functions, then the derivative of their product is given by (uv)' = u'v + uv'.
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