BC Calculus AP Exam 1b 2024 part 1 25 Questions

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Back

Front

What is the average rate of change of the function f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?

Back

The average rate of change is 2.

Front

How do you find the right-hand Riemann Sum with three sub-intervals?

Back

The right-hand Riemann Sum is calculated by evaluating the function at the right endpoints of each sub-interval and summing the areas of the rectangles formed. For this case, the answer is 34.

Front

What are the critical points of the function f(x) = x^3 - 3x^2 + 4?

Back

The critical points are x = 0 and x = 2.

Front

When is the function f(x) = x^2 + 6x + 9 increasing?

Back

The function is increasing on the interval (-3, ∞).

Front

What is the definition of a critical point in calculus?

Back

A critical point is a point on a function where the derivative is zero or undefined.

Front

What is the formula for the average rate of change of a function f(x) on the interval [a, b]?

Back

Front

What is the significance of the Riemann Sum in calculus?

Back

Riemann Sums are used to approximate the area under a curve, which is fundamental in the concept of integration.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing where its derivative is positive and decreasing where its derivative is negative.

Front

What is the relationship between the first derivative and the critical points of a function?

Back

Critical points occur where the first derivative is zero or undefined, indicating potential local maxima or minima.