Please help me solve this function?
f(x)= -4(x-3)^3 (x+1)^2
Sure! To solve the function f(x) = -4(x-3)^3 (x+1)^2, we need to determine the values of x for which the function equals zero. This means we are looking for the x-values that make the function equal to 0.
To begin, let's set f(x) equal to 0 and solve for x:
-4(x-3)^3 (x+1)^2 = 0
Now, we can break down this equation into two separate parts:
-4(x-3)^3 = 0 or (x+1)^2 = 0
Let's solve each part separately:
1. -4(x-3)^3 = 0:
To solve this equation, we can set each factor equal to zero:
x - 3 = 0
Solving for x, we add 3 to both sides of the equation:
x = 3
So, one solution is x = 3.
2. (x+1)^2 = 0:
To solve this equation, we can take the square root of both sides:
x + 1 = 0
Solving for x, we subtract 1 from both sides of the equation:
x = -1
So, another solution is x = -1.
Therefore, the solutions to the equation f(x) = -4(x-3)^3 (x+1)^2 = 0 are x = 3 and x = -1.
These values of x are called the "zeros" or "roots" of the function, as they make the function equal to zero.