The slope of the tangent line to the curve y = 3/x at the point (9 , 1/3) is:

Answer 1

tangent to the curve is the derivative: y' = -3/x^2

at (9,1/3) the slope is y' =-3/(1/3)^2 = -3/9 = -1/3

It's a hyperbola, the branch in the 1st quadrant all slopes are negative. it's -1 when x=y = sqr3 = 1.732

and approaches zero as x approaches infinity. at x=9, it's increasing but approaching zero from the negative side.