Question

Determine the point(s) at which the graph of
the function has a horizontal tangent line. MEDAL WILL BE REWARDED!!!
f(x)=x^2/(x^2+1)

Answer 1

horizontal lines have 0 slope , right ?
so, just differentiate f(x) and equate
f'(x) = 0

Answer 2

So my horizontal line is 0,0?

Answer 3

f'(c) gives the slope of tangent at point c
but the tangent we need is horizontal
so, its slope = 0
thats why we put f'(x) = 0

Answer 4

yes so my final answer is f'(x) is 0,0?

Answer 5

ohh,
let me calculate ...

Answer 6

I think its either 0,1 or 0,0

Answer 7

i get x = 0 too
so, f(0) = 0
and yes, so the point is (x,f(x)) = (0,0) is correct :)

Answer 8

awesome thank you :) More questions to come!

Answer 9

welcome ^_^