## anonymous 4 years ago The function x^5 -5x^4 +5x^3 +10 has only a maximum only minimum both maximum and minimum

1. UnkleRhaukus

the highest order term is $$x^5$$ it will effect the over all shape of the graph

2. anonymous

Plz DON T SOLVE THIS BY GRAPH....ANY OTHER METHOD...

3. UnkleRhaukus

the order of $$x^5$$ is 5 which is an odd number, odd ordered functions

4. anonymous

i'm thinking you mean local maximum and local minimum because the end behaviour of this function is they go to plus/minus infinity.

5. anonymous

Find f'(x). Equate it to zero. Find f''(x). Substitute the values of f'(x) in f''(x), see whether it is negative or positive. If negative, local maximum and if positive, local minimum.

6. anonymous

@apoorvk , @srinidhijha bhai, please say whether I am correct or not.

7. anonymous

I THINK U R CORRECT BUT HOW TO FIND F(X)

8. anonymous

@FoolForMath

9. anonymous

U know differentiation or not @open_study1 ?

10. ajprincess

f(x)= x^5 -5x^4 +5x^3 +10 f'(x)=differentiation of f(x).

11. anonymous

YES

12. anonymous

AFTER DIFERNTIATION WE HAVE TO EQUATE THAT TO 0 IS IT????

13. ajprincess

ya.

14. anonymous

SO IT WILL BE IN X^4 TERMS SO HOW WILL WE SOLVE THAT???

15. ajprincess

Yup. bt u will b abl to factorise it.

16. anonymous

x^4-4X^3+3X^2+10=0

17. anonymous

@ajprincess HOW TO FACTORISE LOL

18. ajprincess

Vat do u get ven u differentiate a number?

19. anonymous

5X^4-20X^3+15X^2+10

20. anonymous

it is wrong..

21. anonymous

x^4-4x^3+3x^2

22. anonymous

SORRY MOT 10 IT IS 0

23. anonymous

x^4-4X^3+3X^2=0

24. ajprincess

Nw can u factorise it?

25. anonymous
26. anonymous

$\Large f''(x)=4x^3-15x^2+6x$

27. anonymous

let it be f(x) differentiate wrt x.........and equate to zero solve for x value again diferrentiate the differentiated one and substitute the x value...... if u get positve value,it has minima and vice-versa

28. anonymous

OK X=0 X= 1 X=3 THEN

29. anonymous

@anusha.p CAN U SHOW IT

30. anonymous

find $\Large f''(0) \quad f''(1)\quad and \quad f''(3)$

31. anonymous

OK THEN

32. anonymous

The function has a minimum value at x = a if f '(a) = 0 and f ''(a) = a positive number. The function has a maximum value at x = a if f '(a) = 0 and f ''(a) = a negative number.

33. anonymous

THAZZZ