The slope of tangent line is first derivation of function.
slope=dy/dx
If you don't know how to find Derivation
in Google type: "calc101"
When you see list of results click on:
calc101com
When page be open click option:
derivatives
In rectacangle type:
x*cos[x]
(exactly in this form) .Then click option DO IT
You will see that first derivation of your function is:
cos(x)-x*sin(x)
Now you must find zero of this expression.
cos(x)-x*sin(x)=0
cos(x)=x*sin(x) Divide with cos(x)
1=x*sin(x)/cos(x)
sin(x)/cos(x)=tan(x)
1=x*tan(x) Diwide with x
1/x=tan(x)
tan(x)=1/x is solution of your problem.
For x≠0, the slope of the tangent to y=xcosx equals zero whenever:
(a) tanx=-x
(b) tanx=1/x
(c) sinx=x
(d) cosx=x
Please help. I have a final tomorrow and I am working diligently to understand every type of problem that may show up on my test. Thank you very much.
1 answer