# Thread: AP Calculus Multiple Choice Questions- Help!

1. ## AP Calculus Multiple Choice Questions- Help!

Hi Everyone, I need some help on a couple of these MC questions for AP Calc AB. Hopefully someone can give me pointers!!

1) Let $\displaystyle f$ and $\displaystyle g$ be twice differentiable functions such that $\displaystyle f'(x) is greater than 0$ for all $\displaystyle x$ in the domain of $\displaystyle f$.
If $\displaystyle h(x)= f(g'(x))$ and $\displaystyle h'(3)=-2$, then at x=3

A. h is concave down
B. g is decreasing
C. f is concave down
D. g is concave down
E. f is decreasing

--------------------------------------------------------------------------

2. If $\displaystyle f$ is differentiable at $\displaystyle x=a$, which of the following could be false?

A. $\displaystyle f$ is continuous at x=a
B. Limit as x approaches a $\displaystyle (f(x)-f(a))/(x-a)$ Exists
C. Limit as x approaches a of f(x) exists
D. f'(a) is defined
E. f''(a) is defined

2. Originally Posted by r2d2
Hi Everyone, I need some help on a couple of these MC questions for AP Calc AB. Hopefully someone can give me pointers!!

1) Let $\displaystyle f$ and $\displaystyle g$ be twice differentiable functions such that $\displaystyle f'(x) is greater than 0$ for all $\displaystyle x$ in the domain of $\displaystyle f$.
If $\displaystyle h(x)= f(g'(x))$ and $\displaystyle h'(3)=-2$, then at x=3

h'(x) = f'[g'(x)] g''(x)

h'(3) = f'[g'(3)] g''(3)

-2 = (some positive value) g''(3)

what sign does g''(3) have to have? and what does that tell you about g(x)?

A. h is concave down
B. g is decreasing
C. f is concave down
D. g is concave down
E. f is decreasing

--------------------------------------------------------------------------

2. If $\displaystyle f$ is differentiable at $\displaystyle x=a$, which of the following could be false?

this is really basic ... you need to check your text/notes on what it means for a function to be differentiable at point.

A. $\displaystyle f$ is continuous at x=a
B. Limit as x approaches a $\displaystyle (f(x)-f(a))/(x-a)$ Exists
C. Limit as x approaches a of f(x) exists
D. f'(a) is defined
E. f''(a) is defined
...

3. Ok, so for the first question, the answer must be D, because g must be negative, which means g must be concave down

For the second equation the answer should be A, because a function could be differentiable but not continuous (ex. #/0)

4. Originally Posted by r2d2
Ok, so for the first question, the answer must be D, because g must be negative, which means g must be concave down

For the second equation the answer should be A, because a function could be differentiable but not continuous (ex. #/0)
that is incorrect ... differentiabilty implies continuity.

http://mathforum.org/library/drmath/view/53637.html