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

Mathematics
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the highest order term is \(x^5\) it will effect the over all shape of the graph
Plz DON T SOLVE THIS BY GRAPH....ANY OTHER METHOD...
the order of \(x^5\) is 5 which is an odd number, odd ordered functions

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Other answers:

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

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