# Increasing/Decreasing/Concave up/ concave down

• Mar 16th 2008, 02:14 PM
stephanie44912
Increasing/Decreasing/Concave up/ concave down
Let f(x)=x(sq.rt. 4-x^2) Find the intervals where f(x) is:

a. increasing
b. decreasing
c. concave up
d. concave down

Then find any:
e. local extrema
f. inflection points

I'm especially having difficulty finding the deriv. of the function and simplifying. Can someone help me solve all the steps??
• Mar 16th 2008, 05:43 PM
Jhevon
Quote:

Originally Posted by stephanie44912
Let f(x)=x(sq.rt. 4-x^2) Find the intervals where f(x) is:

please clarify. do you mean $f(x) = x \sqrt{4 - x^2}$

Quote:

a. increasing
this is where f'(x) > 0

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b. decreasing
this is where f'(x) < 0

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c. concave up
this is where f''(x) > 0

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d. concave down
this is where f''(x) < 0

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Then find any:
e. local extrema
extrema occur where the derivative is zero or the original function is undefined.

to classify extrema (if necessary):

it is a local maximum if f'(x) = 0 and f''(x) < 0

it is a local maximum if f'(x) = 0 and f''(x) > 0

Quote:

f. inflection points
inflection points occur where f''(x) = 0. at times further tests are needed. to make sure it is an inflection, make sure that f''(x) changes signs on both sides of x. that is, if it is negative to the left of x and then positive to the right of x, then x is an inflection point.

Quote:

I'm especially having difficulty finding the deriv. of the function and simplifying. Can someone help me solve all the steps??
as i said, i'm not exactly sure what you function is, but it seems you will need the chain rule here.