Determine the interval on which The function is differentiable :
f(x) = 3x - 5
I know that if f is differntiable on (a,infinity) and the one side limt f(x) -f(a) / x-a exists then its differntiable on [a,infinity)
I found the interval of the function which appears to be (infinty,infinity)
i.e R .. all real numbers
But i really cant find the interval of the derivtive !!!
You answered the question you asked, the function is differentiable for all real values of x
The derivative is the slope of that straight line, 3 , so 3 and only 3
The function f(x) = 3x - 5 is a linear function, and linear functions are differentiable everywhere. Therefore, the interval on which the function is differentiable is the set of all real numbers, or (-∞, +∞).
To determine the interval on which the function f(x) = 3x - 5 is differentiable, we need to check where the function is continuous and has a derivative.
The function f(x) = 3x - 5 is a linear function, and linear functions are continuous and differentiable everywhere. Therefore, the interval on which the function is differentiable is the entire real number line, (-∞, +∞).
To understand why this is the case, it helps to know that linear functions have a constant slope. The derivative of a linear function is its slope, which remains constant across the entire domain. This means that the function has a well-defined derivative at every point in its domain, making it differentiable everywhere.