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Consider f(x)=ax^(4)+cx^(2)+dx+e has no ...

Consider `f(x)=ax^(4)+cx^(2)+dx+e` has no point of inflection. Then which of the following is/are possible? (a) `agt0,clt0` (b) `alt0,cgt0` (c) `a,clt0` (d) `a,cgt0`

A

`agt0,clt0`

B

`alt0,cgt0`

C

`a,clt0`

D

`a,cgt0`

Text Solution

Verified by Experts

The correct Answer is:
3,4
f(x) =`ax^(4)+cx^(2)+dx+e`
`rarr f(x)=12ax^(2)+2c=0`
`rarr x^(2)=(c )/(6a)`
Since the funtion has no point of inflection above equation has no real roots
`rarr c//agt0`
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