Find the x -coordinates of all relative maxima of f(x) f(x)=-(3)/(4)x^4-3x^3+81x^2-37 Answer Attempt 3 out of 4 (4) Additional Solution (- No Solution x=

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 these 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 . The solutions to this equation are , , and .Step 3: Determine which of these critical points correspond to relative maxima.To determine which of these 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 critical point corresponds to a relative minimum.Since , the critical point corresponds to a relative maximum.Since , the critical point corresponds to a relative maximum.Therefore, the x-coordinates of all relative maxima of the function are and .