Find the maximum and the minimum values (if any) of the function $f(x) = 2x^3 +5$.

Neither a maximum nor a minimum value exists.

The correct answer is Option (4) → Neither a maximum nor a minimum value exists.

Given $f(x) = 2x^3 +5, D_f= R$.

Now when $x → ∞, f(x) → ∞$ and when $x → -∞, f(x) → -∞$.

Therefore, $f$ has neither maxima nor minima.

In fact, f is a strictly increasing function for all $x∈R$.