Calculus Formulas - Unit 5 Applications

The first derivative, y', gives the ___ of the function.

• slope

• maximum

• velocity

• concavity

The second derivative, y'', gives the ___ of the function.

• slope

• acceleration

• minimum

• concavity

When y' = 0 or undefined, then the function y ...

• is changing direction

• has a guaranteed extrema

• has a possible extrema

• is changing concavity

When y'' is 0 or undefined, then the function y ...

• is changing direction

• has a guaranteed extrema

• has a possible point of inflection

• is changing concavity

y has a relative maximum when

• y changes from + to -

• y' changes from - to +

• y' = 0

• y' changes from + to -

y has a relative minimum when

• y changes from + to -

• y' changes from - to +

• y' = 0

• y' changes from + to -

Which of the following is a required condition for the Mean Value Theorem?

• f(x) is differentiable on [a, b]

• f(x) is continuous on [a, b]

• f(a) = f(b)

• f'(x) = 0

What is the conclusion of the Mean Value Theorem?

• at some point f'(x) = 0

• f(x) has an average value

• average rate = instant rate

• all values between f(a) and f(b) are represented

g(x) is concave up when

• g(x) is increasing

• g'(x) is positive

• g''(x) is negative

• g'(x) is increasing

g(x) is concave down when

• g(x) is increasing

• g'(x) is positive

• g''(x) is negative

• g'(x) is increasing