How would I find the equation of the tangent to the curve below when the slope of the tangent is 4?

Question

Given: y= 2x - 8/x

thanks

Answer 1

Hi,

Given: y= 2x - 8/x

what does it mean slope?

slope is y' = 2 + 8/x² that is equal 4 then solve equation and find x

2 + 8/x²= 4 -----> 8/x²= 2 ------> x = ±2

Now, when x = 2 ----> y= 0 -----> as a result the equation of tangent line is:

y - 0 = 4 ( x - 2) ====> y = 4x - 8

second time x = -2 -----> y=0 ======> y = 4( x +2)=====> y = 4x + 8

I hope it is useful,

Minoo