How do you find the slope of the indicated point for y=x^2 -4x at x=1

Question

anonymous · Answer

y'=2x-4

y'(1)= 2(1)-4 =-2

slope=-2

anonymous · Answer

slope is dy/dx at x1

so dy/dx= 2x-4
at x1=4
slope= 2-4=-2

anonymous · Answer

and how would one find the equation of the tangent of this function? and moreover the equation of the normal?

anonymous · Answer

$$f(a+h)-f(a)/h$$ my teacher suggests that we use this expression, why is that?

anonymous · Answer

i cant say why that expression is used,but

since slope of the curve at x=1 is -2 , slope of tangent would be 1/2 and it passes through (1,-3). the y coordinate -3 is the value of f at x=1
so its equation is y+3=0.5(x-1)

anonymous · Answer

well he used it as a limit, this is still a bit foggy but maybe its the tiredness, thanks for the clarification