Question

What are the values of constant c for which the line is y=x+c is a tangent to the curve y=3x+2/x?

Answer 1

c=4

Explanation:

A tangent line usally defined by `y=mx+c`.
In your case `m=1` is given.
So to calculate c first we need to find the x value where your function grows with rate 1. To do so just calculate the devirative
`d/dx(3x+2/x)=3-2/x^2` and set it equal to 1
`3-2/x^2=1 |-1 ,+2/x^2`
`2=2/x^2|*x^2/2`
`x^2=1`
`x=1`
if you plug that in into your original function you get
`3*1+2/1=5`
now we know the tangent touches our function at x=1 and y=5
to get to c we need to find the value of our tangent at x=0
which is 4 (you can just go back one since our m is 1)