The function `f(x)=x^(3)+ax^(2)+bx+c,a^(2)le3b` has

Options

A. one maximum value
B. one minimum value
C. no extreme value
D. one maximum and one minimum value

Answer

C

Explanation

Given `f(x)=x^(3)+ax^(2)+bx+ca,a^(2)le3b`
`impliesf'(x)=3x^(2)+2ax+b`
Put `f'(x)=0`
`implies3x^(2)+2ax+b=0`
`impliesx=(-2a+-sqrt(4a^(2)-12b))/(2xx3)=(-2a+-2sqrt(a^(2)-3b))/6`
Since `a^(2) le3b`.
`:.x` has an imaginary value.
Hence no extreme value of x exist.