what is tangent line of f(x) = 6-x^2 and x= -1

Question

 What is the tangent line of f(x) = 6 -x²  at x = -1

Answer 1

Find the derivative of f(x).  Then evaluate the derivative x=-1.

 

f'(x) = -2x

       = -2(-1)

       = 2

 

This is your slope of the tangent line.

 

Then use the point-slope form of a line to get your tangent line. 

 

The given point is (-1, 5).

 

y = m(x - x₁) + y₁

 

y = 2(x + 1) + 5