For k(x)= (-x- 1)(x^2 + 3x - 1)(x+2), find the derivative of k(x) at the point = -2 using the product rule.

The derivative of that product of functions evaluated at the point x=-2 gives "-3"

Step-by-step explanation:

Recall that the derivative of a product of two functions f(x) and g(x) is given by the formula:

(f*g)'= f' * g+ f * g'

So it would be convenient to reduce this product of three functions to a product of just 2, performing (-x-1)*(x+2) = - x^2 - 2x - x -2 = - x^2 -3x -2

therefore we need to find the derivative of x^2 + 3x -1, and the derivative of - x^2 -3x -2  to obtain the

Now, applying the product rule for those two trinomial functions, we get:

which at x = -2 becomes:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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