Question

Calculus, Limits and Continuity Can someone please answer/explain this question? Thank you.

Answer 1

9514 1404 393

Answer:

  (A) -4 and -2

Step-by-step explanation:

The constant in the function tells you f(0) = 5.

You know that the positive leading coefficient means the value of f(x) will be negative for x-values smaller than some number. The offered answer choices indicate the value x = -4 is a lower bound on the value of c. So, -4 < c < 0, for sure.

To further refine the interval, you would need to know f(-2) and/or f(-1).

  f(-2) = (-2)³ -2(-2) +5 = -8 +4 +5 = 1

Then -4 < c < -2.

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I find a graphing calculator to be very helpful locating zeros of polynomials.