anonymous
  • anonymous
The function x^5 -5x^4 +5x^3 +10 has only a maximum only minimum both maximum and minimum
Mathematics
schrodinger
  • schrodinger
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UnkleRhaukus
  • UnkleRhaukus
the highest order term is \(x^5\) it will effect the over all shape of the graph
anonymous
  • anonymous
Plz DON T SOLVE THIS BY GRAPH....ANY OTHER METHOD...
UnkleRhaukus
  • UnkleRhaukus
the order of \(x^5\) is 5 which is an odd number, odd ordered functions

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anonymous
  • 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.
anonymous
  • 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.
anonymous
  • anonymous
@apoorvk , @srinidhijha bhai, please say whether I am correct or not.
anonymous
  • anonymous
I THINK U R CORRECT BUT HOW TO FIND F(X)
anonymous
  • anonymous
@FoolForMath
anonymous
  • anonymous
U know differentiation or not @open_study1 ?
ajprincess
  • ajprincess
f(x)= x^5 -5x^4 +5x^3 +10 f'(x)=differentiation of f(x).
anonymous
  • anonymous
YES
anonymous
  • anonymous
AFTER DIFERNTIATION WE HAVE TO EQUATE THAT TO 0 IS IT????
ajprincess
  • ajprincess
ya.
anonymous
  • anonymous
SO IT WILL BE IN X^4 TERMS SO HOW WILL WE SOLVE THAT???
ajprincess
  • ajprincess
Yup. bt u will b abl to factorise it.
anonymous
  • anonymous
x^4-4X^3+3X^2+10=0
anonymous
  • anonymous
@ajprincess HOW TO FACTORISE LOL
ajprincess
  • ajprincess
Vat do u get ven u differentiate a number?
anonymous
  • anonymous
5X^4-20X^3+15X^2+10
anonymous
  • anonymous
it is wrong..
anonymous
  • anonymous
x^4-4x^3+3x^2
anonymous
  • anonymous
SORRY MOT 10 IT IS 0
anonymous
  • anonymous
x^4-4X^3+3X^2=0
ajprincess
  • ajprincess
Nw can u factorise it?
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=x^4-4x^3%2B3x^2%3D0
anonymous
  • anonymous
\[\Large f''(x)=4x^3-15x^2+6x\]
anonymous
  • 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
anonymous
  • anonymous
OK X=0 X= 1 X=3 THEN
anonymous
  • anonymous
@anusha.p CAN U SHOW IT
anonymous
  • anonymous
find \[\Large f''(0) \quad f''(1)\quad and \quad f''(3)\]
anonymous
  • anonymous
OK THEN
anonymous
  • 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.
anonymous
  • anonymous
THAZZZ

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