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The greph of y=x^3+ax^2+bx+c has no exte...

The greph of `y=x^3+ax^2+bx+c` has no extemun if and only if

A

`a^2=b`

B

`a^2 lt 3b`

C

`a^2 gt 2b`

D

`a^2 gt 2b ^2`

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`y=x^3+ax^2+bx+c rArr dy/dx=3x^2+2ax+b`
Clearly `dy/dx gt 0 if 4a^2-12b lt 0`
`rArr y = f(x)` has no extremum iff `a^2 lt 3b `
Hence, f(x) has no extremum iff `a^2 lt 3b`
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