For the cubic, f(x)=2 x3+9 x2+12 x+1 which one of the following statement, does not hold good?

Question

For the cubic, f(x)=2 x3+9 x2+12 x+1 which one of the following statement, does not hold good? (A) f ( x ) is non monotonic (B) increasing in (-∞,-2) ∪(-1, ∞) and decreasing is (-2,-1) (C) f: R arrow R is bijective (D) Inflection point occurs at x=-3 / 2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/13fe459e49b9af9472184ff81ee3d2ed-.png" /> f ( x )=2 x 3+9 x 2+12 x +1 f prime( x )=6[ x 2+3 x +2]=( x +2)( x +1) text Hence x =-2 text is maxima and x =-1 text is minima f prime prime( x )=2 x +3=0 ⇒ x =-3 / 2 text is the inflection point text obviously f text is non monotonic ∴ f text is many one text hence it is not bijective.

Q. For the cubic, $f (x) = 2 x^{3} + 9 x^{2} + 12 x + 1$ which one of the following statement, does not hold good?

$f (x)$ is non monotonic

increasing in $(- \infty, - 2) \cup (- 1, \infty)$ and decreasing is $(- 2, - 1)$

$f : R \to R$ is bijective

Inflection point occurs at $x = - 3/2$

$f (x) = 2 x^{3} + 9 x^{2} + 12 x + 1$
$f^{'} (x) = 6 [x^{2} + 3 x + 2] = (x + 2) (x + 1)$
$Hence x = - 2 is maxima and x = - 1 is minima$
$f^{''} (x) = 2 x + 3 = 0$
$\Rightarrow x = - 3/2 is the inflection point$
$obviously f is non monotonic$
$∴ f is many one$
$hence it is not bijective.$

Q. For the cubic, f(x)=2x3+9x2+12x+1 which one of the following statement, does not hold good?

f(x) is non monotonic

increasing in (−∞,−2)∪(−1,∞) and decreasing is (−2,−1)

f:R→R is bijective

Inflection point occurs at x=−3/2