How do you find the average rate of change of a function $$f(x)$$ from point a to b?

Use the formula: $$\frac{f(b) - f(a)}{b - a}$$ .

What does the second derivative tell us about a function?

It indicates the concavity of the function and can identify points of inflection.

What is the definition of an integral?

An integral represents the area under a curve defined by a function over a specified interval.

How do you evaluate the integral $$\int x^2 dx$$ ?

$$\frac{x^3}{3} + C$$ , where C is the constant of integration.

What is the average value of a function $$f(x)$$ over the interval [a, b]?

$$\frac{1}{b-a}\int_a^b f(x)dx$$ .

What is the power rule for integration?

For any real number n ≠ -1, $$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$ .

What is the relationship between the first and second derivatives?

The first derivative gives the slope of the tangent line, while the second derivative gives the rate of change of the slope.

What is a critical point in calculus?

A critical point occurs where the first derivative is zero or undefined, indicating potential maxima or minima.

What is the difference between definite and indefinite integrals?

Definite integrals compute the area under a curve over an interval, while indefinite integrals represent a family of functions.

Calculus AB Exam 2024 S1 part 1 Flashcards

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