Question

The number of points at which f(x)=|x^3-7x| is not differentiable is

Answer 1

Given:

f (x) = | x^3 - 7x |

To find:

Find the number of points at which f (x) = | x^3 - 7x | is not differentiable

Solution:

From given, we have a function,

f (x) = | x³ - 7x |

In order to find the points at which a given function is not differentiable, we need to equate the given function to zero.

Therefore, we have,

f(x) = 0

⇒ | x³ - 7x | = 0

x³ - 7x = 0

x (x² - 7) = 0

x = 0 and

x² - 7 = 0

x² = 7

x = √7

Therefore, there are 2 points, x = 0 and x = √7 where, the function f(x) =|x^3-7x| is not differentiable.