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For f(x)=x^(3)+bx^(2)+cx+d, if b^(2) gt ...

For `f(x)=x^(3)+bx^(2)+cx+d`, if `b^(2) gt 4c gt 0` and `b, c, d in R`, then f(x)

A

is strictly increasing

B

is strictly decreasing

C

has a local maxima

D

is bounded

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Let f(x) = ax^(3) + bx^(2) + cx + d, b^(2) - 3ac gt 0, a gt 0, c lt 0 . Then f(x) has

    A
    local maximum at some `x in R^(+)`
    B
    a local maximum at some `x in R^(-)`
    C
    a local minima at x=0
    D
    local minima at some `x in R^(-)` ltbr. `R^(+) = (0, oo), R^(-) = (-oo, 0)`

  • Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0 , where a, b, c, d in R . If f(x) is one-one and onto, then which of the following is correct ?

    A
    `b^(2) < 3ac`
    B
    `b^(2) = 3ac`
    C
    `b^(2) ge 3ac`
    D
    `b^(2)=3c`

  • If f(x) = x^(3) + bx^(2) + cx +d and 0lt b^(2) lt c .then in (-infty, infty)

    A
    f(x) is a strictly increasing function
    B
    f(x) has a local maxima
    C
    f(x) is a strictly decreasing function
    D
    f(x) is bounded

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