Consider the function fx- x sin-x- for x-0 0- for x-0- Then- the number of points in 0-1 where the derivative f-x vanishes is

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Convexity

Consider the ...

Question

Consider the function $f (x) = {\begin{matrix} x sin \frac{π}{x}, f o r x > 0 0, f o r x = 0 \end{matrix}$ . Then, the number of points in $(0, 1)$ where the derivative $f^{'} (x)$ vanishes is

0

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

1

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

2

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

infinite

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

Open in App

Solution

Suggest Corrections

Similar questions

{\begin{matrix} x sin \frac{π}{x} f o r x > 0 0 f o r x = 0 \end{matrix}

(0, 1)

f^{'} (x)

f (x) = {\begin{matrix} x, & for x \leq 0 0, & for x > 0 \end{matrix}

f (x)

x = 0

f

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{t a n^{2} {x}}{(x^{2} - [x]^{2})}, & f o r x > 0 1, & f o r x = 0 \sqrt{{x} c o t {x}}, & f o r x < 0 \end{matrix}

[x]

x

x

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{cos 3 x - cos 4 x}{x^{2}}, f o r x \neq 0 \frac{7}{2}, f o r x = 0 \end{matrix}

x = 0

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{x + | x |}{x}; for x \neq 0 3; for x = 0 \end{matrix}

Join BYJU'S Learning Program