Posted by Anonymous on Tuesday, June 1, 2010 at 6:30pm.
For y=(1/4)x^4(2/3)x^3+(1/2)x^23, 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^32x^2x
...and set it equal to zero to find the points where derivative crosses the xaxis
x^32x^2x=0
I factored and used the quadratic formula, and got (2+sqrt8)/2 and (2sqrt8)/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(x1)(x1) = 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= 1/4x41/3x3+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 ...
 Math  Find the intervals on which the function is increasing, decreasing, ...
 Calculus  For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine ...
 Maths  Let f(x)= x^55x+3 1Find f'(x) and f"(x). 2Find the intervals on which...
More Related Questions