## mathslover Group Title find the minimum value of $$4-5x-4x^2$$. 2 years ago 2 years ago

1. FoolForMath Group Title

For any parabola of the form $$ax^2+bx+c=0$$ the vertex will be at $$\large \left(-\frac b {2a} , -\frac {b^2-4ac}{4a}\right)$$.Equation of line of symmetry will be at $$x=-\frac b {2a}$$ Maximum and minimum values will be at $$\large \left(-\frac b {2a} , -\frac {b^2-4ac}{4a}\right)$$ and $$\large \left(-\frac b {2a} , -\frac {b^2-4ac}{4a}\right)$$ for $$a<0$$ and $$a>0$$ respectively.

2. mathslover Group Title

3. RaphaelFilgueiras Group Title

i think there is no minimum value

4. RaphaelFilgueiras Group Title

it's unbounded

5. FoolForMath Group Title

For this problem there will be no minimum values.

6. mathslover Group Title

can we do this like : 4-5x-4x^2 4-4(x^2+5x/4) 4-4(x^2+5x4 +25/64) + 25/16 ?

7. mathslover Group Title

is this the correct method ?

8. RaphaelFilgueiras Group Title

|dw:1340428823754:dw|

9. RaphaelFilgueiras Group Title

just maximum value

10. mathslover Group Title

4-4(x^2+5x4 +25/64) + 25/16 89/16-4((x+5/8)^2) hence it as min. value of 89/16 at x =-5/8 is it right ?

11. RaphaelFilgueiras Group Title

nope

12. mathslover Group Title

why ?

13. RaphaelFilgueiras Group Title

THIS FUNCTION HAS NO MINIMUM VALUE

14. mathslover Group Title

http://www.wolframalpha.com/input/?i=4-5x-4x%5E2&t=crmtb01 i am getting right according to this but it may be wrong please have a look

15. FoolForMath Group Title

Lets try to plot this function graphically,

16. mathslover Group Title

k

17. RaphaelFilgueiras Group Title

ok try x = 10000

18. FoolForMath Group Title

when do you think the minimum value will be achieved?

19. FoolForMath Group Title

why?

20. mathslover Group Title

can u tell m not soo good

21. RaphaelFilgueiras Group Title

every x you get i will pick one,that that my function will be less than yours

22. FoolForMath Group Title

Yes, for every minimum you find I can find another x which gives a lesser value ...

23. mathslover Group Title

thanks a lot every one