Chapter 4.5, Problem 18E

To determine

To find: If there is a zero of $f\left(x\right)=6x^3+24x^2-54x-3$ between $-6\text{ and }-5$ or not.

Answer to Problem 18E

Yes

Explanation of Solution

Given information: $f\left(x\right)=6x^3+24x^2-54x-3$

Calculation:

  $f\left(x\right)=6x^3+24x^2-54x-3$

  

Yes, because at $x=-6,$ the value is negative and at $x=-5$ the value is positive,

And the function is continuous, there must be a zero

Between $x=-6\text{ and }x=-5$