What does W′(2) > 3 indicate in the context of a water tank filling with water?
AP Calculus Exam Practice - Derivatives Focus I

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Mathematics
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12th Grade
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Hard
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1.
FLASHCARD QUESTION
Front
Back
Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.
2.
FLASHCARD QUESTION
Front
How do you calculate the average rate of change of a function f(x) on a closed interval [a, b]?
Back
The average rate of change is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).
3.
FLASHCARD QUESTION
Front
Given the function f(x) = 3x^2 - x^3, what is the average rate of change on the interval [1, 5]?
Back
The average rate of change is -13.
4.
FLASHCARD QUESTION
Front
What is the significance of a tangent line to a curve at a point?
Back
A tangent line represents the instantaneous rate of change of the function at that point.
5.
FLASHCARD QUESTION
Front
If a line x + y = k is tangent to the graph of y = x^2 + 3x + 1, how do you find the value of k?
Back
Set the derivative of the curve equal to the slope of the line and solve for k.
6.
FLASHCARD QUESTION
Front
What does it mean for a function to be not differentiable at a point?
Back
A function is not differentiable at a point if it has a discontinuity, vertical tangent, or cusp at that point.
7.
FLASHCARD QUESTION
Front
What is the derivative of f(x) = ln(e^(2x))?
Back
The derivative f'(x) = 2.
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