Question

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.

Answer 1

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.