1) where is the function
f(x)= 5 / (2x-4)^3 increasing.
I know the answer is for all of x but I do not know how to get this. I know that you can write the equation as 5(2x-4)^-3
2) Let a, b, and c be fixed with a>0 and let f(x)=ax^2 + bx + c. Which of the following properties is true of the graph of f(x)?
a)f(x) has either a relative max or inflection point
b) f(x) is always concave up
c)f(x) has one inflection point
d) f(x) has one relative max
e) none of these
I know that the anwer is that f(x) is always concave up but I am not sure why.
Thank you for your help!!
What you know on 1 is wrong. If the denominator is increasing, the function is decreasing. But when 2x-4 is decreasing, thenf is increasing. 2x-4 is decreasing when 2x-4<1 or x<2
check that.
2.
f=ax^2+bx+c
f'=2ax+b
f"=2a, but a>o, so f" is always +