consider the function f(X) =`3x^(4)+4x^(3)-12x^(2)`
Y= f(X) increase in the inerval

Options

A. `(-1,0)cup(2,oo)`
B. `(-oo,0)cup(1,2)`
C. `(-2,0)cup(1,oo)`
D. none of these

Answer

3

Explanation

`f(x)=3x^(4)+4x^(3)-12x^(2)`
`therefore f(x)=12(x^(3)+x^(2)-2x)=12x(x-1)(x+2)`
The sign scheme of f(X) is as follows

The graph of the function is as follows

Thus we have
f(-2)=-32 and f(1)=-5
Hence range of hte function is `[-32,oo)`
Also f(x)= a has real roots if `alt-32`