The tangent line to the graph of g(x) = x^3 at the point (x, y) has slope = 3x^2.
g (3) =?
The slope of the curve at x = 3 is?
The equation of the tangent line to the graph of g(x) = x^3 at x = 3 is y =?

Question

The tangent line to the graph of g(x) = x^3 at the point (x, y) has slope = 3x^2.
g (3) =?
The slope of the curve at x = 3 is? 
The equation of the tangent line to the graph of g(x) = x^3 at x = 3 is y =?

myininaya · Answer

g(x)=x^3
g'(x)=3x^2 <-slope=derivative (whatever!)
g'(3) means slope at x=3 
g'(3)=3(3)^2   <- slope at x=3 (we will call this m)
-----
lines have form y=mx+b
we know a point on this line (x,y)=(3,3^3)
plug m,x,y in to find b

anonymous · Answer

thank you for the help!