At the point $x = 0$ , the function $f (x) = x^{3}$ has

local maximum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

local minimum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

both local maximum and minimum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

neither local maximum nor local minimum

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D neither local maximum nor local minimum
Graph of $f (x) = x^{3}$

Hence at $x = 0, f (x)$ has
Neither local maximum nor minima
i.e., it is point of inflection.

Suggest Corrections

Similar questions

x = 0

f (x) = x^{3} + 1

Which of the following function has a point of inflection at x = 0 ?

f (x) = {\begin{matrix} x^{3} - 8 & 2 < x < \infty x - 2 & - \infty < x \leq 2 \end{matrix}

∣ ∣ x^{3} ∣ ∣

f (x) = x^{3 / 5} (4 - x), x \in R^{+} \cup {0}

Join BYJU'S Learning Program