Find the x-coordinates of all relative maxima of f(x) f(x)=(3)/(5)x^5+12x^4+60x^3+3 Answer Attempticut of 4 (C) Additional Solution No Solution z=1

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 derivative of is given by: Step 2: Set the derivative equal to zero and solve for . The solutions to this equation are: Step 3: Determine which of these points correspond to relative maxima.To determine which of these points correspond to relative maxima, we need to evaluate the second derivative of at each point.The second derivative of is given by: Now, let's evaluate at each of the critical points: Since , we cannot determine whether is a relative maximum or minimum. We need to use the first derivative test or the second derivative test to determine this.Using the first derivative test, we can see that the sign of changes from positive to negative as increases through . Therefore, is a relative maximum.Using the second derivative test, we can see that and . Therefore, and are relative minima.Therefore, the x-coordinate of the relative maximum of is .