Final answer:
The points on the graph where the tangent line is horizontal are (2/5, 5).
Step-by-step explanation:
The graph of the function f(x) = 5x² - 4x + 5 represents a parabola. To find the points on the graph where the tangent line is horizontal, we need to find the values of x where the derivative of the function is equal to zero.
The derivative of f(x) is f'(x) = 10x - 4. Set f'(x) = 0 and solve for x: 10x - 4 = 0 ➝ 10x = 4 ➝ x = 4/10 ➝ x = 2/5.
Therefore, the points on the graph where the tangent line is horizontal are (2/5, f(2/5)). Plug in x = 2/5 into the original function to find the y-coordinate: f(2/5) = 5(2/5)² - 4(2/5) + 5 = 20/25 - 8/5 + 5 = 2/5 - 8/5 + 5 = 5.