Calc Vocab (Units 1 through 4)

The difference quotient is equivalent to all of the following EXCEPT

• The slope of the secant line

• The average rate of change

• The derivative

The derivative gives the

• Average rate of change

• Instantaneous rate of change

The derivative gives

• The slope of the tangent line

• The slope of the secant line

When the first derivative is positive, the function is always

• Increasing

• Decreasing

• Concave up

• Concave down

When the first derivative is negative, the function is always

• Increasing

• Decreasing

• Concave up

• Concave down

When the second derivative is negative, the function is always

• Increasing

• Decreasing

• Concave up

• Concave down

When the second derivative is positive, the function is always

• Increasing

• Decreasing

• Concave up

• Concave down

Values that make the first derivative 0 and points where the first derivative is undefined are collectively referred to as

• critical points

• Points of inflection

• Zeros of the function

• Extrema

True or false: all critical points are extrema

• True

• False

This theorem states that when a function f(x) is continuous on a closed interval [a,b] and the end points have different outputs, then there exists a value c on the interval where f(c) equals a particular value between f(a) and f(b).

• IVT

• MVT

• 1st Derivative Test

• 2nd Derivative Test