Thursday

August 21, 2014

August 21, 2014

Posted by **Phil** on Wednesday, November 14, 2007 at 12:13am.

cos x - x = f(x)

I am told to find the relative extrema. I am also told to use the Second Derivative Test where applicable.

My question is how do I solve this problem, and how do I know when to use the Second Deriv test?

Thanks!

- Calculus -
**drwls**, Wednesday, November 14, 2007 at 2:52amPoints where the first derivative is zero are relative maxima if the second derivatve is negative and relative minima if the second derivative is positive.

In your case, df/dx = 0 when f'(x) = -sin x -1 = 0; sin x = -1

That happens when x = 3 pi/2.

At that point, f''(x) = -cos x = 0

So the second derivative fails to show if is a maximum or minimum. 3 pi/2 could be an inflection point, where the curve flattens out and then resumes its downward trend

- Calculus -
**Phil**, Wednesday, November 14, 2007 at 8:52pmCan't i figure out if its increasing or decreasing using the first derivative test?

What is the point of the second derivative test?

**Related Questions**

Calculus - Find the relative extrema, if any, of the function. Use the second ...

Calculus - 1. Find all relative extrema of the function f(x)=x^(6/7)-3. Use the ...

Calculus - Find the relative extrema and absolute extrema if any. Use the first ...

Applied Calculus - Find the relative extrema, if any, of the function. Use the ...

Math - Find the relative extrema, if any, of the function. Use the second ...

math - Find the relative extrema, if any, of the function. Use the second ...

math - Find the relative extrema, if any, of the function. Use the second ...

calculus - Find the relative extrema of f(x) = -2x^2 + 4x + 3 I don't know how ...

calculus - Find the critical point(s) of the function. Then use the second ...

calculus - Find the critical point(s) of the function. Then use the second ...