a The function f is decreasing over which intervals Choose a

(a) The function f is decreasing over which intervals? Choose all (-infinity, -7) (-7, -5) (-2, 3) (-5, 3) (6, 8) (b) The function f has local minima at which x-values? If there is separate them with commas. (c) What is the sign of the leading coefficient of f?

Solution

a) Decreasing :
When we look from left to right, the graph must go downward
This happens over x = -7 to -5
Then over x = -2 to 3
Then over 6 to 8

So, (-7,-5)
(-2,3)
(6,8)

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b) Minima :
These are clearly at x = -5 , x = 3 and x = 8

x = -5 ,3 , 8

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c)
Clearly here degree = ODD because the graph goes in opposite directions at the extreme ends

Notice on the left end, it goes down
And on the right end, it soars upward

This is definitive of ODD degree, POSITIVE leading coefficient

So, POSITIVE