Final answer:
To find values of x where the slope of y=f(x) is 0, determine the function's derivative and solve for x where the derivative equals 0. For a linear function y=a+bx, the slope b is constant; a slope of 0 across all x values occurs if b=0. A function like y=x^2 has a positive decreasing slope for x>0.
Step-by-step explanation:
The slope of a curve y=f(x) is determined by the derivative f'(x). When the slope is 0, it means that the curve is not rising or falling at that point, essentially indicating a horizontal tangent line. This occurs at points where the curve has a local maximum or minimum. Therefore, to find the values of x where the slope of the curve is 0, we must find the derivative of the function and then solve for x where f'(x) = 0.
In the case of a linear function, such as y = a + bx, finding the slope is straightforward because it is constant throughout the line. As per the given equation, b is the slope. If b = 0, then the line is horizontal, and the slope is 0 everywhere. Thus, for a linear function, if its slope coefficient (b) is 0, the slope will be 0 for all values of x. If a function has a positive value at x = 3 with a positive, yet decreasing slope, it suggests that the derivative of the function is positive and decreasing as x increases. The function y = x2 fits this description because its slope (derivative 2x) is positive and decreasing for x > 0.