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Calculus/Inflection Point

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Expert: Scotto - 6/21/2009


Question
Does f(c)= (c+2)^3 -2 have an inflection point?  If so, where is it located?

a) Yes, at (-2, -2)
b) Yes, at (2, -2)
c) Yes, at (8, -2)
d) no

Answer
It is known that f"(c) = 0 at an inflection point.

It can be seen that f'(c) = 3(c+2)^2.

Now we have to multiply by the derivative of what is inside the parenthesis, but that is 1, so its been done already.

It can be seen that f"(c) = 6(c+2), so the second derivate is a line.
Not that it matters what the second derivative is, only where
f"(c) = 0.

Since there is an x + 2 in f"(c), we need x + 2 = 0,
which means that x = -2.

Putting -2 back into the function gives us
(-2 + 2)^3 - 2 = 0^3 - 2 = -2.

The answer is yes, (-2, -2).

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

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I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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