Find the maximum and the minimum values (if any) of the function $f(x) = 2x^3 +5$.
Answer & explanation
Correct answer: option 4
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 $x∈R$.