Question

What are all values of x for which the function f defined by f(x)=x3+3x2−9x+7 is increasing ?

Answer 1

Answer:

C. $x < -3$ or $x > 1$.

Step-by-step explanation:

Let $f(x) = x^{3}+3\cdot x^{2}-9\cdot x +7$, the first derivate of the function is:

$f'(x) = 3\cdot x^{2}+6\cdot x -9$ (1)

By the Quadratic Formula, we determine the roots of this polynomial:

$x_{1} = 1$, $x_{2} = -3$

And the factorized form of the polynomial is:

$(x-1)\cdot (x+3) > 0$

By law of Signs, the polynomial is increasing when $x-1 > 0$ and $x +3 > 0$ or $x-1 < 0$ and $x+3 < 0$, which means that:

$x < -3$ or $x > 1$

Therefore, the right answer is C.