Find a function whose derivative is a constant k
Any linear function would do
How about
f(x) = 4x + 5
f ' (x) = 4
Since the derivative of a function represents the slope of that function, and the slope of a straight line is constant, the slope of the function I gave is always 4
To find a function whose derivative is a constant k, we can start by considering the general form of a function in terms of its derivative. Let's denote the function as f(x), and its derivative as f'(x).
We know that if f'(x) is a constant k, then it must be independent of x. In other words, the derivative of f(x) with respect to x is a constant.
To find f(x), we can integrate the constant k with respect to x. The integral of a constant with respect to x is simply the constant multiplied by x.
So, to find the function f(x) whose derivative is a constant k, we integrate k with respect to x:
f(x) = kx + C
where C is an arbitrary constant of integration.
Hence, any function of the form f(x) = kx + C, where k is a constant and C is any real number, will have a derivative equal to the constant k.