Final answer:
The point at which the graph of the function has a tangent line with a slope of -5 is (-5/2, 9.25).
Step-by-step explanation:
The question is asking for the point, if any, at which the graph of the function has a tangent line with a slope of -5. To determine this point, we need to find the derivative of the function and set it equal to -5. The given function is y = x² + 3, so we need to find dy/dx (the derivative of y with respect to x). Taking the derivative of the function, we get dy/dx = 2x.
Next, we set 2x = -5 and solve for x: 2x = -5 → x = -5/2.
Therefore, the point at which the graph of the function has a tangent line with a slope of -5 is (-5/2, (-5/2)² + 3) = (-5/2, 9.25).