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
[tex]f(x)=4x^3-12x^2-x+15[/tex]
we will plug x=-2
[tex]f(-2)=4(-2)^3-12(-2)^2-(-2)+15[/tex]
now, we can simplify it
[tex]f(-2)=-32-12\cdot \:4-\left(-2\right)+15 [/tex]
[tex]f(-2)=-63 [/tex]
so,
[tex]f(-2)=-63 <0[/tex]
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
