Find an equation of the line tangent to the graph of

Question

Find an equation of the tangent line to the graph of 

 

y=(-6x)/(1-8x)     

 

at the point (0,0)

 

y=?

Answer 1

First you need to find the derivative of your function. This is needed to find the slope of the tangent line.

 

y = (-6x) / (1-8x)   use quotient rule

y' = [ (-6x)' (1-8x) - (6x) (1-8x)' ] / (1-8x)² = [ -6(1-8x) ] / (1-8x)² = (-6 + 48x ) / (1-8x)²

 

Now, substitute x= 0 from the point of tangency into the derivative/slope function:

slope at (0,0) = m = (-6 + 48(0) ) / (1 - 8(0) )² = -6 / 1 = -6

 

Last, substitute slope m = -6 and point (0,0) into point-slope form of a linear equation y - y₀ = m( x - x₀ ):

y - 0 = -6( x - 0)

y = -6x is the equation of the tangent line

 

 

Check: graph your original function & tangent equation in the same window and you'll see them touching