What is f(x) = (2x^3)+(x^2)-x+1 derivative value when x=-1

To find the derivative of the function f(x) = 2x^3 + x^2 - x + 1, we can differentiate each term separately. The derivative of a polynomial term ax^n is given by d(ax^n)/dx = nax^(n-1). Applying this rule to each term in f(x), we have: f'(x) = d/dx(2x^3) + d/dx(x^2) - d/dx(x) + d/dx(1) = 6x^2 + 2x - 1 + 0 (since the derivative of a constant is zero) Now, to find the derivative value when x = -1, we substitute x = -1 into f'(x): f'(-1) = 6(-1)^2 + 2(-1) - 1 = 6(1) - 2 - 1 = 6 - 2 - 1 = 3 Therefore, when x = -1, the derivative of the function f(x) = 2x^3 + x^2 - x + 1 is equal to 3.