Question

Let F be the function given by F(x)= IxI-2/(x-2)

a.) Find all zeros of F
b. Find F'(1).
c. Find F'(-1)
d.Find the range of F.

I am mostly having trouble on b and c, a and d I can do just fine. Any help is appreciated thank you.

Answer 1

do you know the formula for the derivative?

Answer 2

f'(x)= f(x+h)-f(x)/h and the ppwer rule. I think I can also split this function into 2 equations, it's just the absolute value that is messing me up.

Answer 3

when you place your x+h in the function, it will just have an absolute around it, really the absolute doesn't matter until you get to the end, and if there happens to be a negative there then it wouldn't really be negative. does that make sense?

Answer 4

It kind of makes sense, my teacher wanted me to split the function into two separate functions though.

Answer 5

that just means that the the |x|-2 will split up and they will both be under (x-2)

Answer 6

f'(x) = x / sqrt(x^2) + 2 /(x-2)^2

f'(1) = 1 + 2 / (-1)^2 = 3

Answer 7

f'(-1) = -1 / 1 + 2 / 9 = -1 + 2/9 = -7/9

Answer 8

Thank you guys, I'm going to try and work out the full process now.

Answer 9

yw