Graph the function y = x3 + 3x2 – x – 3. which lists all of the turning points of the graph?

(-1, 0)

Step-by-step explanation:

Jim, please use the symbol " ^ " to indicate exponentiation:

y = x^3 + 3x^2 – x – 3.  Thanks.

A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa).  To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.

Given y = x^3 + 3x^2 – x – 3,

          dy/dx = 3x^2 + 6x - 1

           d²y

          = 6x + 6            and this is zero at x = -1.

           dx²

We can easily show that the 2nd derivative changes sign at x = -1.

Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).

step-by-step explanation:

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.