the derivitive is just the slope
minimum happens when the derivitive goes from negative to positive, imagine a slope of the function, the minimum is where the slope goes from neative to positive, and to get there, it has to pass through 0
max happens when the derivitive goes from positive to negative
increaseing is when the derivitive is positive
so, based on what you said, the slope of f(x) is 0 at x=-3, x=1 and x=2 since those are where the derivitive is 0 (derivitive is just the slope)
A and B are wrong because the derivitive isn't 0 at those points
C is correct because increasing means that the derivitive is positive, and so therefo since the only hoirontal place in between 1 and 2 is 1.5, it must remain positive throughout and not dip down, C is right
D is wrong then
answer is C
Rewrite it in the form a^2 - b^2, where a = 5x and b = 8
(5x)^2 - 8^2
Use the Difference of Squares; a^2 - b^2 = (a + b)(a - b)
<u>= C. (5x - 8)(5x + 8)</u>
