Derivative of a Polynomial Function

Question

Determine equations for two lines that pass through the point (1,-5) and are tangent to the graph of y=x^2-2.

Answer 1

y = x^2 -2

 

slope = dy/dx = 2x

slope at x(1) = 2(1) = 2

 

slope intercept form

y = mx + b

 

at y = -5, x=1, m = 2

 

-5 = 2(1) + b

b= -7

 

equation of tangent

 

y = 2x -7

:)