AP Calculus Unit 1-4 Review

Front

When is the function f(x)=x²+6x+9 increasing?

Back

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

Front

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

Back

f'(x) = 2/x.

Front

Find the second derivative of the function: f(x) = 2x - 5x⁶.

Back

f''(x) = -150x⁴.

Front

TRUE OR FALSE? If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

Back

TRUE by Intermediate Value Theorem.

Front

On the unit circle, sine is represented by the:

Back

y-coordinate.

Front

What is the definition of a derivative?

Back

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

Front

What does the Intermediate Value Theorem state?

Back

If a function is continuous on a closed interval [a, b], and N is any number between f(a) and f(b), then there exists at least one c in (a, b) such that f(c) = N.

Front

What is the first derivative test used for?

Back

To determine the local maxima and minima of a function.

Front

What is the relationship between the first and second derivatives?

Back

The first derivative indicates the slope of the function, while the second derivative indicates the concavity of the function.

Front

What is the definition of a critical point?

Back

A critical point occurs where the first derivative is zero or undefined.