Find the x -coordinates of all relative maxima of f(x) f(x)=(3)/(5)x^5+12x^4+60x^3+3

To find the x-coordinates of all relative maxima of the function , we need to find the critical points of the function and then determine which of those points correspond to relative maxima.Step 1: Find the derivative of the function.The derivative of is given by: Step 2: Set the derivative equal to zero and solve for x. The solutions are: Step 3: Determine which of the critical points correspond to relative maxima.To determine which of the critical points correspond to relative maxima, we need to evaluate the second derivative of the function at each critical point.The second derivative of is given by: Now, let's evaluate the second derivative at each critical point:For : For : For : Since the second derivative is positive at and , these points correspond to relative minima. Therefore, there are no relative maxima for the given function.Therefore, the x-coordinates of all relative maxima of are .