Thursday

January 29, 2015

January 29, 2015

Posted by **Frank** on Friday, March 4, 2011 at 1:48pm.

- calculus -
**MathMate**, Sunday, March 6, 2011 at 7:14amFirst we calculate

f'(x)=4*((8-2*x)/(2*sqrt((8-x)*x))+1)

Equate it to zero and solve for x

f(x)=0 =>

((8-2x)/(2sqrt((8-x)x))+1)=0

(8-2x)/(2sqrt((8-x)x))=-1

(8-2x)=-2sqrt((8-x)x)

Square both sides:

(8-2x)^2=4(8-x)*x)

Solve the quadratic to get

x= 4±2√2.

Verify both roots (because we squared) and reject x=4-2√2

That leaves us with

x=4+2√2.

Calculate f"(x):

-(64sqrt(8x-x²))/(x^4-16x^3+64x^2)

Verify that f"(x) <0 at x=4+√2 and hence a maximum.

**Answer this Question**

**Related Questions**

calculus - Please help with this. I submitted it below but no one responded. I ...

calculus - Please help with this. I need the first derivative of f(x)=4(x+...

Calculus - Use a symbolic differentiation utility to find the derivative of the ...

Calculus - I need help with finding first and second derivative--simplify your ...

calculus - Use the function defined below to calculate the indicated derivative...

Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...

English - Can any kind person proof this please Change the following from the ...

calculus - Find the first and second derivative - simplify your answer. y=x/4x+1...

Applied Calculus - Find the first and second derivative of the function: x/(7x+...

Calculus--> bobpursley - How do you get m=0? from taking the second ...