Table of Contents
Is a function differentiable if the derivative is 0?
Differentiability in higher dimensions If all the partial derivatives of a function exist in a neighborhood of a point x0 and are continuous at the point x0, then the function is differentiable at that point x0. is not differentiable at (0, 0), but again all of the partial derivatives and directional derivatives exist.
Is square root of x differentiable at 0?
Left and right-hand limits are the same, the limit must therefore exist and f(x) is thus differentiable at x0=0. According to the solution the limit does not exist, thus f(x) not differentiable at x0=0 .
Is the function 0 continuous?
f(x)=0 is a continuous function because it is an unbroken line, without holes or jumps. All numbers are constants, so yes, 0 would be a constant.
Which of the following function f/x is not differentiable at x 0?
Answer is (d) Hence, function x + |x| is not differentiatable at x = 0.
Is the function x=0 differentiable at x = 0?
Yes it is differentiable at x=0. To check that first you have to define the function for x>0 and x<0. But since you have to check first order differentiability so in both cases when you differentiate it and puts the limit of x as 0 it will turns out to be 0.so left hand limit=RHL=0.
What is the derivative of x^3 at x = 0?
The easiest way to show this to consider the functions y = x^3 and y = (-x)^3 being the right and left sides of the graph. The derivative of y = x^3 is 3x^2, and its value at x = 0 is 0.
What is the value of $f(x)?
Differentiable, as the derivative will always be 0 Continuous, as it is just a horizontal line with no breaks Polynomial, as it can be written as $f(x) = 0 = (1x^n – 1x^n)$
Is the function $f(x)=0$ a polynomial?
The function $f(x)=0$ is a special case of $f(x)=c$ where $c$ is a constant. The same statements are true for $f(x)=c$ for any constant $c$ which are considered as polynomials of degree $0$