Need help with problem, difference quotients: slope of y=ln(x) close to x=4

[RightyBoyWilson]

So the problem is:
"Use the difference quotient with small intervals to estimate the slope of f(x) = ln(x) in the vicinity of x = 4"

I'm pretty sure i'm suppose to plug 3.999 and 4.001 into the (f(x+h) - f(x))/h thing but I'm not sure how to properly deal with the natural log and whatnot.

Any help is appreciated

P.S. Sorry if the font is all funky, it looks weird on mobile so I'm just sticking with the default and hoping it works.

 

[Dr.Peterson]

So the problem is:
"Use the difference quotient with small intervals to estimate the slope of f(x) = ln(x) in the vicinity of x = 4"

I'm pretty sure i'm suppose to plug 3.999 and 4.001 into the (f(x+h) - f(x))/h thing but I'm not sure how to properly deal with the natural log and whatnot.

I think you just need to plug it all into a calculator and see what you get. I don't think they have anything tricky in mind.

So, taking x=4 and h=0.001, what is (ln(4+0.001) - ln(4))/0.001 ? Then try a few more small values for h, such as -0.001 and 0.0001. You'll get a good sense of what the limit might be.

 

[pka]

So the problem is:
"Use the difference quotient with small intervals to estimate the slope of f(x) = ln(x) in the vicinity of x = 4"
I'm pretty sure i'm suppose to plug 3.999 and 4.001 into the (f(x+h) - f(x))/h thing but I'm not sure how to properly deal with the natural log and whatnot

Have a look at this.

 

[RightyBoyWilson]

Thanks!

It makes total sense now, ya'll are friggin legends!