Chapter 3: Calculus

Question 1

Derivatives can be found on what pages in the handbook?

Answer 1

48

Question 2

The first derivative is calculated to determine where the critical points might be. Critical points are located where the first derivative = ____.

Answer 2

zero (f’(a)=0 for x=a)

Question 3

For a function f(x) with an extreme point at x=a, if the point is a maximum, then the second derivative is ____.

Answer 3

Negative

Question 4

For a function f(x) with a critical point at x=a, if the point is a minimum, then the second derivative is ____.

Answer 4

Positive

Question 5

There is a point of inflection when f’‘(a) = __ for a function f(x) with f’(x) = 0 at x=a.

Answer 5

0

Question 6

Derivatives can be taken with respect to only one independent variable at a time. If a function has more than one independent variable at a time, a ________ can be found.

Answer 6

Partial derivative with respect to one of the independent variables.

Question 7

When should L’Hopital’s rule be used?

Answer 7

When the numerator and denominator of the expression are indeterminate at the limit point (either 0 or infinite)

Question 8

Integration is the inverse of differentiation. What are the 2 types of integrals?

Answer 8

definite (specific range) and indefinite (unrestricted and called also antiderivatives)

Question 9

The centroidal moment of inertia is the ____ possible moment of inertia for the area.

Answer 9

Smallest

Question 10

If the moment of inertia is known with respect to one axis, the moment of inertia with respect to another parallel axis can be calculated from the ____

Answer 10

parallel axis theorem