Derivatives Plz Help I'm close to dropping but this is required

Question

let f(x) = 1/x. Compute f ' (-1)

answer: ________

Use this to find the equation of the tangent line to the hyperbola y = 1/x at the point (-1,-1.000).

The equation of this tangent line can be written in the form y = mx + b. Determined m and b

m = __________

b = _________

Answer 1

For f(x)=1 f'(x) = -1/x² using the quotient rule. and f'(-1)= -1. So for the problem were y=1/x dy/dx = -1/x² and the slope at the point (-1, -1000) is -1. Use the straight line equation y=mx + b to find the tangent at the point in question. So -1000 = - (-1) + b then b = -1000 -1 = -1001 and m= -1. So the tangent line is y= -x-1001.