Sunday

December 21, 2014

December 21, 2014

Posted by **Aoi** on Friday, June 19, 2009 at 8:58am.

1. Show that the function f(x)= x^3 - 3x^2 + 9x - 5 is increasing with x for all real values of x.

f'(x)=3x^2-6x+9

=3(x^2-2x+3)

=3[x^2 - 2x + (-2/2)^2 + 3 - (-2/2)^2]

= 3[ (x-1)^2 + 2]

=3(x-1)^2 + 6

?!! The correct answer is supposed to be f'(x)=3(x-1)^2 is ≥0 for all real values of x. Did i do the completing square wrongly?? This same thing happened with the second question

2. Show that f(x) = -2x^2 + 3x^2 - 2x + 4 decreases for all real values of x.

The correct answer for this one is f'(x) = -6(x-1/2)^2 - 1/2 <0 for all real values of x

- Maths integration -
**bobpursley**, Friday, June 19, 2009 at 9:11am1. You did it correctly.

if the first term (x-1)^2 is positive for all x, then that term +6 is positive for all x.

2. Your f' does not match the degree of f(x). I don't know what you meant.

**Answer this Question**

**Related Questions**

Algebra 2 - Completing the square method allows you to solve any quadratic ...

Completing the square - Please show the procedure for answering this quadratic ...

Integration - 1. [integration] (3x+7sin(x))^2 dx i tried 3 different methods of ...

maths - Px^2-(2p+q)x+(p+q)=0 solve by completing of square method

Algebra - I was given this answers to a problems I solved but I do not ...

Algebra - I was given this answers to a problems I solved but I do not ...

maths --plse help me.. - solve the following equation by method of completing ...

maths - The method for completing the square can be used to write the expression...

math,correction - Is this correct now. Problem #1 solve by completing the square...

Algebra - Completing the square method allows you to solve any quadratic ...