1. The problem asks: Which of the following functions is not differentiable? 2. The functions given are: - $f(x) = mx + b$, a linear function. - $f(x) = (x + 3)^4$, a polynomial function. - $f(x) = 1985$, a constant function. - $f(x) = |x|$, the absolute value function. - "None of these" as an option. 3. Let's analyze each one: - $f(x) = mx + b$ is differentiable everywhere because it's a linear function with derivative $f'(x) = m$. - $f(x) = (x + 3)^4$ is differentiable everywhere being a polynomial function. - $f(x) = 1985$ is differentiable everywhere; its derivative is $0$. - $f(x) = |x|$ is differentiable everywhere except at $x=0$ because the function has a "corner" or cusp there, where the left-hand and right-hand derivatives differ. 4. Therefore, the function that is not differentiable is $f(x) = |x|$. Final answer: $f(x) = |x|$ is not differentiable at $x=0$.