If y = x3 + x2 + x + 1, then y

Question

If y = x3 + x2 + x + 1, then y (A) has a local minimum (B) has a local maximum (C) neither have a local minimum nor local maximum (D) None of these

Tardigrade Admin · Accepted Answer

Let f(x) = y = x3 + x2 + x+ 1. Then, f'(x ) = 3x2 + 2 x + 1. For a maximum or minimum, we have f'(x) = 0 ⇒ 3x2 + 2x+ 1 = 0 But, this equation gives imaginary values of x. So, f'(x) ≠ 0 for any real value of x. Hence, f(x) does not have a maximum or minimum.

Q. If y=x3+x2+x+1, then y

has a local minimum

has a local maximum

neither have a local minimum nor local maximum

None of these

Let f(x)=y=x3+x2+x+1. Then, f′(x)=3x2+2x+1. For a maximum or minimum, we have f′(x)=0⇒3x2+2x+1=0 But, this equation gives imaginary values of x. So, f′(x)=0 for any real value of x. Hence, f(x) does not have a maximum or minimum.

Q. If $y = x^{3} + x^{2} + x + 1$ , then $y$