SOLUTION: State approximately the intervals on which f (x) = x4 - 4x3 - 22x2 + 52x - 7 is increasing and on which f (x) = x4 - 4x3 - 22x2 + 52x - 7 is decreasing. Round your answers to the n

Question 302151: State approximately the intervals on which f (x) = x4 - 4x3 - 22x2 + 52x - 7 is increasing and on which f (x) = x4 - 4x3 - 22x2 + 52x - 7 is decreasing. Round your answers to the nearest tenth.
I really don't know how to start this problem. Can you tell me how to do it & I will do the math?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you need to find the maxima and minima

setting the first derivative equal to zero will give you the x values

this function is shaped roughly like a "W"

starting on the left-hand side of the "W"
___ the function is decreasing on the downward stroke
___ then increasing on the first inside upward stroke
___ then decreasing on the next inside downward stroke
___ then finally increasing on the last outside upward stroke

the points where the strokes intersect are the boundries between the increasing and decreasing intervals

remember that the outsides strokes go to infinity on the x-axis; one positive and one negative
___ they both go to positive infinity on the y-axis

in case you haven't had any calculus
___ the first derivative is ___ 4x^3 - 12x^2 - 44x + 52
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