## open_study1 3 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. open_study1

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. dpaInc

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

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.

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

7. open_study1

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

8. open_study1

@FoolForMath

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. open_study1

YES

12. open_study1

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

13. ajprincess

ya.

14. open_study1

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. open_study1

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

17. open_study1

@ajprincess HOW TO FACTORISE LOL

18. ajprincess

Vat do u get ven u differentiate a number?

19. open_study1

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

20. cinar

it is wrong..

21. cinar

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

22. open_study1

SORRY MOT 10 IT IS 0

23. open_study1

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

24. ajprincess

Nw can u factorise it?

25. cinar
26. cinar

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

27. anusha.p

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. open_study1

OK X=0 X= 1 X=3 THEN

29. open_study1

@anusha.p CAN U SHOW IT

30. cinar

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

31. open_study1

OK THEN

32. cinar

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. open_study1

THAZZZ