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Question: For the function: f(x) = -5(2x + 1) (x - 2) 2 (x - 6) I was able to answer the following about this function: Dominant term is -10x 4 The...

Question:


For the function: f(x) = -5(2x + 1) (x - 2)2 (x - 6)


I was able to answer the following about this function:


Dominant term is -10x4


The graph starts low and ends low. The roots are -1/2, 2 (bounces off), and 6.


I was able to sketch the graph without a calculator, roughly, and could see that the domain is {x e R}. From the answers section of the textbook, I saw that the range is {y e R, y < or equal to 500}. So the highest y value for the graph is 500.


My concern is, how is it possible to determine the maximum value of y (500) without a calculator? I believe there is a method in calculus but my course is a grade12 Advanced Functions course for Ontario, Canada and calculus is not taught.


Please help. If a calculus method is all that is available (short of using a calculator) please explain.

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Examples:
01. The function f (x ) = 2x3 - 3x - 36x + 10 has
a maximum value at x =
Sol:
f (x) = 6x2 - 6x - 36 = 0
=&gt; x? -x - 6=0
.. x = 3, -2
ful (x) = 12x - 6
f (3) = 30 &gt; 0
=&gt;
f (x) has...

IMG_20190419_233506.jpg

Working Rule to find maxima and minima:
Let f (x) be the given function
Step 1: Find f (x)
ENGINEER
Step 2: Equate f(x) to zero to obtain the
stationary points.
Step 3: Find f (x) at each...

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