Calculus: Tangent line

Question

Find an equation of the tangent line to the graph of f(x)=1/x^4 

a) at (1,1) 

b) at (3,1/81)

c) at (-2,1/16)

Answer 1

f(x) = 1/x⁴ = x^-4

 

f'(x) = -4x^-5 = -4/x⁵

 

a.  slope of tangent at (1,1) is f'(1) = -4

 

     Equation of tangent:  y - 1 = -4(x - 1)

 

                                         y = -4x + 5

 

Parts b. and c. are done in a similar manner.