Question

The maximum value of the function $x^3+x^2+x-4$ is

• A. 127
• B. 4
• C. Does not have a maximum value
• D. None of these

Answer 1

The correct option is C Does not have a maximum value

Given function be $f\left(x\right)=x^3+x^2+x-4$.
Differentiating with respect to x, we get
$f^{\prime }\left(x\right)=3x^2+2x+1$
Here, discriminant $=2^2-4\left(3\right)\left(1\right)=4-12=-8<0$
So, the real roots will not exist for $f^{\prime }\left(x\right)=3x^2+2x+1$
Thus, $f^{\prime }\left(x\right)\ne 0$ at real values of x.
Hence, f(x) does not have maximum value.