1. fint the lines that are tangent and normal to the curve at (1,1)
im guessing that i have to use the definition of a derivative, and substitute f(x) and x in the equation with one, and solve it?
what about the normal line?
Correct, take the first derivative of and solve
The normal is always perpendicular to the tangent and so the product of their gradients must be -1: where = the gradient at that point and
In both cases use the equation of a straight line formula:
where is a coordinate. In your case this is (1,1)