Question

Suppose That S(X) = (4 - X)(X + 6)?

Find all critical values of S. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas. Critical value(s) - 0,4000/27

Answer 1

The critical value of the function S(x) = (4 - x)(x + 6) is found by setting its first derivative equal to zero. The derivative S'(x) = -2x - 2 when set to zero gives the critical value x = -1.

Step-by-step explanation:

To find the critical values of the function S(x) = (4 - x)(x + 6), we need to set its first derivative equal to zero and solve for x. The critical values are the x-values where the first derivative equals zero or where the derivative is undefined.

First, we'll find the derivative of S with respect to x. Applying the product rule:

S'(x) = (4-x)'(x+6) + (4-x)(x+6)'

S'(x) = (-1)(x+6) + (4-x)(1)

S'(x) = -x - 6 + 4 - x

S'(x) = -2x - 2

To find the critical values, we set S'(x) to zero:

-2x - 2 = 0

2x = -2

x = -1

Thus, the critical value of the function S(x) is x = -1.