Respuesta :

Answer:


Step-by-step explanation:

y intercept occurs when x = 0

here it is -36.

As the last number is -36,   6 may be a  x intercept here

f(x) = 6^3 - 11*36 - 36*6 - 16 - 0  so x = 6 is a x-intercept ( zero) of this graph.

Dividing the function by (x - 6) gives x^2 - 5x + 6

which = (x - 2)(x - 3) so the other 2 zeroes are 2 and 3.

The coefficient of x^3 is positive so the curve will rise from the left passing through y = - 36 and  forming 2 turning points, cutting the x axis at  x = 2, 3 and 6 and will rise to the right. There will be a local maximum between x = 2 and x = 3 and a local minimum between x = 3 and x = 6.

altavistard

Answer:

y-intercept:  (0, -36); x-intercepts:  (2,0), (3,0), (6,0)

Step-by-step explanation:

Hint:  Please use " ^ " to denote exponentiation:  f(x) = x^3 − 11x^2 + 36x − 36

I guessed that a root of this function is x = 6, with the implication that (x-6) is a factor of f(x) = x^3 − 11x^2 + 36x − 36.  

This can be proven using synthetic division.  The coefficients of the quotient are 2, 3 and 6.  Thus, the x-intercepts are (2,0), (3,0) and (6,0).  Letting x = 0 leaves us with y= -36, so the y-intercept is (0, -36)

The graph begins in Quadrant III, increasing as x increases.  It enters Quadrant I briefly and then it reverses direction and heads downward a bit, and finally turning up and increasing indefinitely in Quadrant I.


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