AP Calculus BC exam rev

Front

What is the definition of a slope field?

Back

A slope field is a graphical representation of the solutions to a first-order differential equation, showing the slope of the solution curve at various points in the plane.

Front

What is Euler's method in numerical analysis?

Back

Euler's method is a numerical technique for solving ordinary differential equations (ODEs) by approximating solutions using tangent line segments.

Front

What is the formula for the average value of a function on an interval [a, b]?

Back

Front

What is the relationship between the derivative and the slope of a function?

Back

The derivative of a function at a point gives the slope of the tangent line to the function at that point.

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Back

Front

What is the second derivative of a function?

Back

The second derivative of a function is the derivative of the derivative, indicating the rate of change of the rate of change, often related to the concavity of the function.

Front

Back

Front

What is the significance of initial conditions in differential equations?

Back

Initial conditions specify the value of the function or its derivatives at a particular point, allowing for the determination of a unique solution to a differential equation.

Front

Back

Front

What is the concept of concavity in calculus?

Back

Concavity refers to the direction of the curvature of a function; a function is concave up if its second derivative is positive and concave down if its second derivative is negative.

Tags

CCSS.HSF.IF.B.4