Derivative questions

Question

(2x^2+2x-3)/(x^2(x-3)^2 

 

tangent line at x=-1

 

please help me find the equation line .. I only got to the function part 

Answer 1

You need to evaluate the original function at x=-1.  This will give you the point (x₁ , y₁) and is the point the tangent line passes through.

 

Then, evaluate the derivative at x=-1.  Call this f'(-1) and is your slope of the tangent line.

 

 

Now you can use the point-slope form of a line:

 

y = f'(-1)(x - x₁) + y₁