SOLUTION: Find the slope of the tangent line at the given point then write the equation of the tangent line. f(x)=4/x, x=5 Ans y=-4x/25+8/5 I keep getting this answer 4x + 25y = 40

Algebra ->  Functions -> SOLUTION: Find the slope of the tangent line at the given point then write the equation of the tangent line. f(x)=4/x, x=5 Ans y=-4x/25+8/5 I keep getting this answer 4x + 25y = 40      Log On


   

Question 290635: Find the slope of the tangent line at the given point then write the equation of the tangent line.
f(x)=4/x, x=5
Ans y=-4x/25+8/5
I keep getting this answer 4x + 25y = 40
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+4%2Fx
y+=+4%2Fx
y+=+4x%5E%28-1%29
Find the slope (dy/dx) at x = 5
dy%2Fdx+=+-4x%5E%28-2%29
dy%2Fdx+=+-4%2Fx%5E2 and at x = 5,
dy%2Fdx+=+-4%2F25, so...
y+=+%28-4%2F25%29x%2Bb Substitute x = 5 and y = 4/5
4%2F5+=+%28-4%2F25%29%285%29%2Bb
4%2F5+=+%28-4%2F5%29%2Bb Solve for b. Add 4%2F5 to both sides.
8%2F5+=+b so finally...
highlight%28y+=+%28-4%2F25%29x%2B8%2F5%29