Question For the function f(x) = 5(2x + 1) (x 2)2 (x 6)I

Question

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 -10×4

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.

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