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ratelena [41]
3 years ago
13

Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the shape of the grap

h.
Mathematics
1 answer:
kap26 [50]3 years ago
3 0
1) y-intercept => x = 0, => y = f(0) = 0 - 0 + 0 - 36 = -36

2) x-intercept => y = 0 => factor the function (start by dividing by x -2)

f(x) = (x-2)(x-3)(x-6) =0 => x =2, x = 3, x = 6 (these are the x-intercepts)

3) critical points:

between x = 2 and x = 3, there is a local maximum

between x =3 and x = 6 there is a local minimum

3) Shape.

The function comes growing from - infinity.

In the third quadrant the function is negative (it does not pass throuhg the second quadrant)

It enters to the fourth quadrant intercepting the y-axis at y = -36. It continues growing and intercepts the x-axis at x = 2.

 It continues increasing until a maximum local positive value, starts to decrease, intercepts the x-axis at x = 3, continues decreasing, becomes negative, gets a local minimum in the fourth quadrant, starts to increase, intercepts the x-axis at x = 6, becomes positive, and continues growing.
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