Find the equation of the tangent to the curve defined by y = x + ln x that is perpendicular to the line defined by 3x + 9y = 8

Question

anonymous · Answer

First we want to get the slope which we will get from this equation

 3x + 9y = 8 

Can you tell me what the slope of this line is?

anonymous · Answer

i just need the steps and the answer. i already learned the material back in september, just need some refreshing for the exam i have next week.

anonymous · Answer

Oh ok First get the slope.

Then find the derivative  of  x + ln x

Set the derivative equal to the slope and solve for x.

Plug the x into the original equation y = x + ln x to get y

Now you have your slope m  and point (x,y)

Use point slope form 

(y-y1)=m(x-x1)

where x1 and y1 is your point

anonymous · Answer

You can leave it as it is or simplify it to y-intercept form.

anonymous · Answer

Get it?

anonymous · Answer

word, now i remember.

thanks.

anonymous · Answer

The slope is the negative reciprocal of the slope of this line 

3x + 9y = 8 

just fyi