# AP Calculus Multiple Choice Questions- Help!

• Dec 29th 2009, 04:06 PM
r2d2
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

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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
• Dec 29th 2009, 04:18 PM
skeeter
Quote:

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

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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

...
• Dec 29th 2009, 05:17 PM
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)
• Dec 29th 2009, 05:21 PM
skeeter
Quote:

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