Question 1:

Atthe point x=a, we know that f''(a) > 0. Which of the following statements must be true?

f(a) > 0

f'(a) > 0

f'(a) < 0

None of these

Question 2:

Which of the following statements is True?

The Local Maximum of a function isalwaysalso the highest point on a function.

The Local Maximum of a function issometimesalso the highest point on a function.

The Local Maximum of a function can alsosometimesbe the lowest point on a function

The Local Maximum of a function isneveralso the highest point on a function.

Question 3:

For some position function,it is known that on the interval a

Both v(t) and a(t) are positive from a to b

There is not enough information here

v(t) (the velocity funtion) is positive from a to b

a(t) (the acceleration funtion) is positive from a to b

Question 4:

For aparticular function f(x), it is known that at x=a, f'(a) = 0 and f''(a) > 0. Which of the following statements is true?

f(x) hasa Local Maximum at x=a

f(x) hasan Inflection Point at x=a

We cannot make a determination based on the provided information

f(x) hasa Local Minimum at x=a

Question 5:

The pendulum of a grandfather clock starts at its leftmost position at time t=0. It then begins to swing to the right.Ifh(t) represents the height of the pendulum, which of the following best illustrates the initial conditions of this situation?

h(t) < 0 and h(t) > 0

h(t) > 0 and h(t) < 0

h(t) < 0 and h(t) < 0

h(t) > 0 and h(t) > 0