Thursday

April 2, 2015

April 2, 2015

Posted by **Juliet** on Thursday, January 19, 2012 at 10:48pm.

Any help would be awesome...thanks!

(i know that the relative extrema come from critical values from y' and points of inflection come from y'')

- calculus -
**Reiny**, Friday, January 20, 2012 at 12:02amdy/dx = y' = ln((x^4)/8) + x(4/x)

= ln ( (x^4)/8 ) + 4

y '' = 4/x

for relative extrema, y' = 0

ln ((x^4)/8) = 0

x^4 / 8 = e^0 = 1

x^4 = 8

x = ± 8^(1/4)

plug in those values into y = ...

for pts of inflection, 4/x = 0 ----> no solution

thus, no points of inflection

- calculus -
**Steve**, Friday, January 20, 2012 at 10:29amAnd yet, y'' changes from - to + as x increases through 0, so while y is discontinuous at x=0, there

**appears**to be an inflection point there.

To get the limit of y at x=0,

y(0) = 0*(-oo)

setting t=1/x and using L'Hopital's rule a bit, we can see that the limit is 0.

**Answer this Question**

**Related Questions**

Relative Extrema: AP Calculus - Consider the function f(x)= (3/4)x^4-x^3-3x^2+6x...

calculus - Find all relative extrema and points of inflection of the function: f...

calculus - Find any relative extrema and any points of inflection if they exist ...

Calculus - Find the x-values of all points where the function below has any ...

APCalculus - For the function y=4-2x^2+1/6x^4 find the following: Domain x and y...

Calculus A - Find all relative extrema and points of inflection for the ...

APCalculus - For the function y=2sin(x)-cos^2(x) on [0, 2pi] find the following...

Calculus - Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x ...

Calculus - Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x ...

Calculus A - Find all relative extrema and points of inflection for the ...