show that the function f(x) = x3+x2+x+1 has neither a maximum value nor a minimum value - Maths - Application of Derivatives

Question

show that the function f(x) = x3+x2+x+1 has
neither a maximum value nor a minimum value

Lovina Kansal · Accepted Answer

Dear student
We have,f(x)=x3+x2+x+1f'(x)=3x2+2x+1For maximum and minimum value, we must havef'(x)=0⇒3x2+2x+1=0⇒x=-2±4-126⇒x=-2±-86 where b2-4ac=4-12=-8 which is negative
 So, it has no real roots
So, there is no minimum or maximum value
Regards