Find an equation of the tangent line to the graph of the following function f at the specified point.

Question

f(x)=10x/x^2-6; (4,4) (This is the equation)

Answer 1

I'm going to assume you meant the problem to be written as 10x/(x^2-6). Using the quotient rule, the derivative of the function f(x) is -10(x^2+6)/(x^2-6)^2. Plugging in the value x = 4 gives the tangent lines slope at x = 4. So m = -2.2. Now use that and the point (4,4) in the equation y = mx+b. So 4 = 4(-2.2) + b making b = 12.8. Your equation is then y = -2.2x + 12.8