For 9–10, use a graphing calculator to graph the function. then use the graph to determine the number of turning points and the number and type (global or local) of any maximum or minimum values. 9. f(x)=x(x+2)(x+1) 10. f(x)=(x-1)3 (power to)(x+1)

Please, see the attached graphs

Step-by-step explanation:

9. f(x)=x(x+2)(x+1)

It has a local maximum of 0.385 at x = - 1.577

It has a local minimum of - 0.385 at x = - 0.423

It has an inflection point at x = - 1

10. f(x)=(x-1)^3 (x+1)

It has a global minimum of - 1.688 at x = - 0.5

It has two inflection points at x=0 and at x=1

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.