What are all values of x for which the function f defined by f(x)=x3+3x2−9x+7 is increasing ? (A) −3 (B) −1 (C) x<−3 or x>1
(D) x<−1 or x>3
(E) All real numbers.

The correct option is an option (c).

Given:

The given function is,

Computation:

The function is increasing when .

Now, differentiating the given function with respect to up to first order we get,

So, the sign function is,

 Therefore, when

So, is increasing on or

Hence, the correct option is an option (c).

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C. or .

Step-by-step explanation:

Let , the first derivate of the function is:

(1)

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

,

And the factorized form of the polynomial is:

By law of Signs, the polynomial is increasing when and or and , which means that:

or

Therefore, the right answer is C.

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step-by-step explanation: