- #1

- 20

- 0

What is the local Max, local Min, when is the function increasing and decreasing!

the function is:

G(x)= x - 4 sqrt[x]

You should upgrade or use an alternative browser.

- Thread starter rumaithya
- Start date

- #1

- 20

- 0

What is the local Max, local Min, when is the function increasing and decreasing!

the function is:

G(x)= x - 4 sqrt[x]

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 964

Here, I suggest that you write the function as G(x)= x- 4x

The maximum value will occur where G'= 0 or G' does not exist (look carefully at x=0).

The function is increasing where G'> 0 and decreasing where G'< 0.

If this is really x- 4 sqrt("greatest integer less than or equal to x"), then it is not differentiable. I would recommend you graph it carefully.

- #3

- 175

- 0

- #4

ShawnD

Science Advisor

- 668

- 1

rumaithya said:What is the local Max, local Min, when is the function increasing and decreasing!

the function is:

G(x)= x - 4 sqrt[x]

First find the domain of the function. You know the function is only real when x >= 0 (or at least in my reality )

Secondly, find the derivative. I got this as the derivative:

[tex]1 - 2x^{\frac{-1}{2}}[/tex]

Just by looking at the equation you were given, you know G(x) is going to be negative at low x values. Since it starts decreasing, the local maximum is 0. To find the local minimum, set the derivative G'(x) equal to 0, solve for x, then fill that x value into your original formula G(x).

To find when the function is increasing or decreasing, substitute x values into the derivative. Sub in an X value slightly less than where the derivative equals 0, then sub in an X value slightly more than where the derivative equals 0.

I got these answers:

Local Max G(x) = 0

Local Min G(x) = -4

Decreasing when 0 > x > 4

Increasing when 4 > x > infinity

- #5

Zurtex

Science Advisor

Homework Helper

- 1,120

- 1

Not always. For example G = x^6, at x = 0 there is a minimum yet G ' ' = 0 at x = 0.gazzo said:point of infelction when G ' ' = 0

- #6

ShawnD

Science Advisor

- 668

- 1

Zurtex said:Not always. For example G = x^6, at x = 0 there is a minimum yet G ' ' = 0 at x = 0.

That's still an inflection point though.

- #7

Zurtex

Science Advisor

Homework Helper

- 1,120

- 1

It is?ShawnD said:That's still an inflection point though.

I seem to have the wrong idea on what an inflection is then, could you please explain.

- #8

ShawnD

Science Advisor

- 668

- 1

Depends on definition I guess.

- #9

mathwonk

Science Advisor

Homework Helper

2020 Award

- 11,154

- 1,349

Share: