Posted by **Anonymous** on Tuesday, June 1, 2010 at 6:30pm.

For y=(1/4)x^4-(2/3)x^3+(1/2)x^2-3, find the exact intervals on which the function is

a. increasing

b. decreasing

c. concave up

d. concave down

Then find any

e. local extreme values

f. inflection points

---

I thought it'd be better to find extreme values first, then you can find the points where the function is increasing or decreasing. (I'll worry about concavity and inflection points later, since that's second derivative)

So I found y':

x^3-2x^2-x

...and set it equal to zero to find the points where derivative crosses the x-axis

x^3-2x^2-x=0

I factored and used the quadratic formula, and got (2+sqrt8)/2 and (2-sqrt8)/2, or -.414 and 2.414. Oh, and zero too because I factored out an x.

So my problem is that the answers (which were given to me ahead of time to check my work) don't match my work. Apparently y is increasing from [0, infinity) and decreasing from (-infinity, 0], and none of the points I found from finding y'.

Can you find what I did wrong?

Thanks!

- Calculus -
**Reiny**, Tuesday, June 1, 2010 at 8:09pm
Your derivative is wrong,

you should have

y' = x^3 - 2x^2 + x

When I set x^3 - 2x^2 - x = 0, I get

x(x^2 - 2x + 1 ) = 0

x(x-1)(x-1) = 0

x = 0 or x = 1

take it from there.

- Calculus -
**Anonymous**, Tuesday, June 1, 2010 at 8:12pm
Oh wow, such a simple mistake throws off everything, haha. Thanks

## Answer this Question

## Related Questions

- grade 12 AP calculus - for f(x= -1/4x4-1/3x3+2x, use analytic method to find the...
- increasing decreasing and more - How to analytically find the intervals on which...
- Calculus (urgent!!) - Please answer the following questions about the function f...
- Calculus (pleas help!!!) - Please answer the following questions about the ...
- Calculus (pleas help!!!) - Please answer the following questions about the ...
- Math - For y= (3x)/(2e^x+e^-1), use graphing techniques to find the approximate ...
- Calculus - let f(x)=x^3(e^-x) Answer using calculus, use graphing calculator ...
- Calculus - For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine ...
- calculus - Please help me solve. I think increase = concave up and decrease = ...
- Maths - Let f(x)= x^5-5x+3 1-Find f'(x) and f"(x). 2-Find the intervals on which...