Finding the tangent's gradient at 1!

Sep 2016
3
0
Denmark
Hello,

I am currently learning about calculus.
I have an assignment where I have to find out which point on the curve f(x)=x/x^2+1 the tangent have gradient at 1. I am not sure on how to calculate this, so if anybody can help me, it would be much appreciated :)
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
Hello,

I am currently learning about calculus.
I have an assignment where I have to find out which point on the curve f(x)=x/(x^2+1) the tangent have gradient at 1. I am not sure on how to calculate this, so if anybody can help me, it would be much appreciated :)
are you trying to find the gradient at $x = 1$, or where the tangent to the curve has gradient = $1$ ?

in either case, use the quotient rule to find $f'(x)$ ...

$f'(x) = \dfrac{(x^2+1)(1)-(x)(2x)}{(x^2+1)^2}$

if you're trying to find the gradient at $x=1$, then evaluate $f'(1)$

if you're trying to find where the gradient equals $1$, then solve $f'(x)=1$ for $x$.

oh, and use grouping symbols to make your expression clear
 
Last edited:
Sep 2016
3
0
Denmark
I am trying to find where the gradient equals 1. Thank you for your answer!
But what do you mean by using "grouping symbols"? Like brackets or?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
But what do you mean by using "grouping symbols"? Like brackets or?
you posted
... point on the curve f(x)=x/x^2+1 ...
that expression could be interpreted as $\dfrac{x}{x^2} + 1$ in the absence of grouping symbols.

Grouping symbols that are used most often are (parentheses) and/or [brackets], like so ...

f(x) = x/(x^2+1)