Generate a continuous and differentiable function f(x) with the following properties: . f(x) is decreasing at x=-6--6 . f(x) has a local minimum at x=-2=-2 . f(x) has a local maximum at x=2=2 We are told that there is a local max and local min at x=2, and x=-2. This information gives us the critical points. We know critical points happen when the first derivative is zero. So, we have the first derivative. f' (x) = (x - 2)(x+ 2) =x2-4 Now, we know that the function is decreasing at x=-5. This means that f ' (-6) should be negative. Now, let's check that this is the case. f'(-6) = 36 -4 = 32. Because this is not negative, this means that with the function we have now, it is increasing at x=-6. To fix this, we can make the first derivative negative. f' (x) =-x2+4