AP Calculus AB

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What is the definition of an Initial Value Problem (IVP)?

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An Initial Value Problem (IVP) is a differential equation along with a specified value, called the initial condition, at a given point. It typically involves finding a function that satisfies the differential equation and meets the initial condition.

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How do you find the limit of a function as it approaches a certain value?

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To find the limit of a function as it approaches a certain value, you can substitute the value into the function, simplify if necessary, and check if the function approaches a specific number.

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What is the Fundamental Theorem of Calculus?

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What is the definition of a derivative?

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The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero. It represents the slope of the tangent line to the function at that point.

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What does it mean for a function to be concave up?

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A function is concave up on an interval if its second derivative is positive over that interval, indicating that the slope of the tangent line is increasing.

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What is the product rule for differentiation?

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What is the chain rule for differentiation?

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