Question

The value -2 is a lower bound for the zeros of the function shown below f(x)=4x^3-12x^2-x+15

true or false

Answer 1

The answer is true

--------------------------------------------------

We already know that each and every zero is always between a positive and a negative number.

We get f(-3)=-63, which is a negative number.

As a result, this is the lower bound and the answer is true

Answer 2

We are given

The value -2 is a lower bound for the zeros of the function shown below f(x)=4x^3-12x^2-x+15

So, firstly, we will find value of f(x) at x=-2

we will plug x=-2 into f(x)

we get

`f(x)=4x^3-12x^2-x+15`

we will plug x=-2

`f(-2)=4(-2)^3-12(-2)^2-(-2)+15`

now, we can simplify it

`f(-2)=-32-12\cdot \:4-\left(-2\right)+15`

`f(-2)=-63`

so,

`f(-2)=-63 <0`

we know that any zeros always lies between positive and negative value

Here , we got f(-3)=-63 ...which is negative value

so, this is lower bound

Hence , this is TRUE