The function f(x) = e^x is differentiable at all points?
Practice Questions
Q1
The function f(x) = e^x is differentiable at all points?
True
False
Only at x = 0
Only at x = 1
Questions & Step-by-Step Solutions
The function f(x) = e^x is differentiable at all points?
Step 1: Understand what differentiable means. A function is differentiable at a point if it has a defined slope (derivative) at that point.
Step 2: Identify the function given in the question, which is f(x) = e^x.
Step 3: Recognize that e^x is an exponential function. Exponential functions are known to be smooth and continuous.
Step 4: Check if there are any points where the function might not be differentiable. Since e^x is defined for all real numbers, there are no such points.
Step 5: Conclude that since e^x is smooth and continuous everywhere, it is differentiable at all points.
