Podcast
Questions and Answers
If a function $f$ is differentiable in an interval $I$, what arises as a natural question?
If a function $f$ is differentiable in an interval $I$, what arises as a natural question?
- Given $f'$ at each point of $I$, can we determine the function? (correct)
- How to find the maximum of $f$ in interval $I$?
- Can $f$ have a vertical asymptote in interval $I$?
- What is the area under the curve of $f$ in interval $I$?
What is the original motivation for the concept of the derivative in Differential Calculus?
What is the original motivation for the concept of the derivative in Differential Calculus?
- Calculating the area of the region bounded by the graph of the functions
- Defining tangent lines to the graphs of functions (correct)
- Defining the slope of secant lines
- Finding the anti-derivatives of a function
What are the functions that could possibly have given function $f'$ as a derivative called?
What are the functions that could possibly have given function $f'$ as a derivative called?
- Indefinite integrals
- Anti-derivatives (correct)
- Definite integrals
- Primitive functions
What is the original motivation for the concept of Integral Calculus?
What is the original motivation for the concept of Integral Calculus?
What is the formula that gives all the anti-derivatives of a function called?
What is the formula that gives all the anti-derivatives of a function called?
Flashcards
Recovering the original function from its derivative
Recovering the original function from its derivative
Finding the original function if we know its derivative at each point in an interval.
Tangent line to a function's graph
Tangent line to a function's graph
Finding the slope of a line that touches a function's graph at a specific point.
Anti-derivatives of a function
Anti-derivatives of a function
Functions whose derivative is the given function.
Area under a function's curve
Area under a function's curve
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Indefinite integral
Indefinite integral
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