Unit 4 Review - AP Calculus

Front

What is a point of inflection?

Back

A point of inflection is where a function changes its concavity, specifically from concave up to concave down or vice versa.

Front

Use a linear approximation centered at x = 2 to find f(2.5) for f(x) = x^3 - x.

Back

f(2.5) ≈ 11.5 using linear approximation.

Front

If a function has a second derivative that is negative, what does that indicate?

Back

It indicates that the function is concave down.

Front

Where does the function f(x) = 2x^3 - 9x^2 + 12x - 3 have relative max/min values?

Back

Relative max at x = 1 and relative min at x = 2.

Front

How fast is the area of an oil spill increasing when the radius is 5 m and the radius increases at 5 m/min?

Back

The area is increasing at 50π m²/min.

Front

What is the definition of a derivative?

Back

The derivative of a function represents the rate of change of the function with respect to a variable.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if its derivative is positive over an interval.

Front

What is the relationship between the first and second derivatives in determining concavity?

Back

The first derivative indicates increasing or decreasing behavior, while the second derivative indicates concavity.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by A = πr², where r is the radius.

Front

What is the significance of critical points in calculus?

Back

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