For the cubic, f( x )= x 3-3 x 2+6 x +2006, the statement which does not hold good, is

Question

For the cubic, f( x )= x 3-3 x 2+6 x +2006, the statement which does not hold good, is (A) f( x ) is monotonic increasing ∀ x ∈ R (B) f: R arrow R is injective as well as surjective. (C) slope of the tangent at the point of inflection is 3 . (D) f ( x ) is non monotonic with exactly one real root.

Tardigrade Admin · Accepted Answer

Correct answer is (d) f ( x ) is non monotonic with exactly one real root.

Q. For the cubic, $f (x) = x^{3} - 3 x^{2} + 6 x + 2006$ , the statement which does not hold good, is

$f (x)$ is monotonic increasing $\forall x \in R$

$f : R \to R$ is injective as well as surjective.

slope of the tangent at the point of inflection is 3 .

$f (x)$ is non monotonic with exactly one real root.

Correct answer is (d) $f (x)$ is non monotonic with exactly one real root.

Q. For the cubic, f(x)=x3−3x2+6x+2006, the statement which does not hold good, is

f(x) is monotonic increasing ∀x∈R

f:R→R is injective as well as surjective.