Final answer:
The graph of f(x) = x² sin(x) has a horizontal tangent when the derivative of the function is equal to zero. The equation 2xsin(x) + x²cos(x) = 0 needs to be solved to find the values of x where the derivative is zero.
Step-by-step explanation:
The graph of the function f(x) = x² sin(x) has a horizontal tangent when the derivative of the function is equal to zero. Taking the derivative of f(x), we get f'(x) = 2xsin(x) + x²cos(x). To find the values of x where the derivative is zero, we need to solve the equation 2xsin(x) + x²cos(x) = 0. Unfortunately, it is not possible to find a simple, exact algebraic solution for this equation. However, we can use numerical methods or technology to approximate the values of x