AP Calc AB Semester 1 Review Flashcard

Front

What is the formula for the surface area of a sphere?

Back

A = 4πr²

Front

How do you determine if a function has a relative maximum using its derivative?

Back

f'(x) has a change in values from positive to negative.

Front

What is the relationship between the rates of change of the sides of a right triangle when one side is changing?

Back

Use related rates to set up an equation based on the Pythagorean theorem.

Front

What does it mean for a function to be increasing?

Back

A function f(x) is increasing on an interval if f'(x) > 0 for all x in that interval.

Front

What is the derivative of f(x) = x² + 6x + 9?

Back

f'(x) = 2x + 6.

Front

At what point does the function f(x) = x² + 6x + 9 reach its minimum?

Back

At x = -3.

Front

What is the significance of f'(x) = 0?

Back

It indicates a potential relative maximum or minimum.

Front

How do you find the rate of change of the surface area of a sphere as its radius changes?

Back

Use the formula dA/dt = dA/dr * dr/dt.

Front

What is the relationship between the height and base of a ladder leaning against a wall?

Back

The height, base, and length of the ladder form a right triangle.

Front

What is the second derivative test for concavity?

Back

If f''(x) > 0, the function is concave up; if f''(x) < 0, it is concave down.