Calculus for business and econ HELP

[hiramoby]

Find all relative extrema of the function

. Use the Second-Derivative Test when applicable.

Answer

	a.	The relative maximum is .
	b.	The relative minimum is .
	c.	The relative maximum is .
	d.	The relative minimum is .
	e.	The relative maximum is .

 

[tkhunny]

Those instructions are very helpful. You will need to calcuoate a 1st and a 2nd derivative.

 

[HallsofIvy]

Since you are given such a problem, presumably you know that "extrema" for a function, f(x), occur at "critical points"- where the derivative, f'(x), is 0 or does not exist. Such a critical point will be a "local maximum" if the second derivative, f''(x), is negative and a "local minimum" if it is positive. If the second derivative is 0, that test does not tell you anything.

So now the ball is back in your court- what are the first and second derivatives of \(\displaystyle \frac{16}{x^2+ 1}= 16(x^2+ 1)^{-1}\)?