Final answer:
To find the values of x at which the curve y = f(x) has a tangent line parallel to the line y = mx + c, set the derivative of y = f(x) equal to m and solve for x.
Step-by-step explanation:
In order for the curve y = f(x) to have a tangent line parallel to the line y = mx + c, the slope of the curve at that point must be equal to the slope of the line. Since the slope of a line is constant, we can find the values of x that make this true by setting the derivative of y = f(x) equal to m.
Let's say the derivative of y = f(x) is f'(x). We can set f'(x) = m and solve for x. This will give us the values of x at which the curve has a tangent line parallel to y = mx + c.
For example, if the equation of the line is y = 2x + 1, we set f'(x) = 2 and solve for x to find the values.