Answer:
x = -3
Explanation:
You want the x-coordinate of the relative maximum of f(x) = x³ +4x² -3x +1.
Extrema
The x-coordinates of the relative extrema of the function will be those values of x where the derivative of the function is zero.
f'(x) = 3x² +8x -3 = (x +3)(3x -1)
The derivative is zero where its factors are zero, at x = -3 and x = 1/3.
Relative maximum
The leading coefficient of this cubic is positive, so the function values generally increase from left to right. That means the relative maximum will have the lowest x-coordinate: x = -3
The x-coordinate of the relative maximum is -3.