Show that y = x is tangent to the graph of f at the origin.

To show that the line y = x is tangent to the graph of a function f at the origin, we need to show that the derivative of the function f at the origin is equal to the slope of the line y = x, which is 1.

Step 1: Find the derivative of the function f(x). This is usually denoted as f'(x) or df/dx.

Step 2: Evaluate the derivative at the origin, i.e., find the value of f'(0).

Step 3: If f'(0) = 1, then the line y = x is tangent to the graph of the function f at the origin. This is because the derivative of a function at a point gives the slope of the tangent line at that point, and the slope of the line y = x is 1.

If f'(0) ≠ 1, then the line y = x is not tangent to the graph of the function f at the origin.

To show that the line y = x is tangent to the graph of a function f at the origin, we need to show that the derivative of the function f at the origin is equal to the slope of the line y = x, which is 1.

Step 1: Find the derivative of the function f(x). This is represented as f'(x).

Step 2: Evaluate the derivative at the origin, i.e., find the value of f'(0).

Step 3: If f'(0) = 1, then the line y = x is tangent to the graph of the function f at the origin. This is because the derivative of a function at a point gives the slope of the tangent line at that point, and the slope of the line y = x is 1.

If f'(0) ≠ 1, then the line y = x is not tangent to the graph of the function f at the origin.