Question

F(x) =3x^3-2x^2+x-5 f`(-1)

Answer 1

xⁿ = n * xⁿ⁻¹

x' = 1

F'(x) = 9x² - 4x + 1

F'(-1) = 9 * 1 - 4 * (-1) + 1 = 9 + 4 + 1 = 14

Answer 2

To find the derivative of the function F(x) = 3x^3 - 2x^2 + x - 5, we need to apply the power rule. The power rule states that the derivative of x^n with respect to x is nx^(n-1).

So, for F(x) = 3x^3 - 2x^2 + x - 5:

F'(x) = d/dx (3x^3) - d/dx (2x^2) + d/dx (x) - d/dx (5) = 3 * d/dx (x^3) - 2 * d/dx (x^2) + 1 * d/dx (x) - 0 (since the derivative of a constant is 0) = 3 * 3x^2 - 2 * 2x + 1 = 9x^2 - 4x + 1

Now that we have the derivative F'(x), we can find the value of the derivative at x = -1 by plugging in x = -1 into the expression for F'(x):

F'(-1) = 9(-1)^2 - 4(-1) + 1 = 9(1) + 4 + 1 = 9 + 4 + 1 = 14

So, F'(-1) = 14.