i) Find the points on the graph of y=(1/3)x^3 -5x-(4/x) at which the slope of the tangent is horizontal.
ii) find the slope of the demand curve D(p)=20/((sqrt p -1)), p>1, at point (5,10).
I need help with the two questions above, I'm doing practice questions with the slope of tangent but these last two questions I'm stuck on. Please help me or guide me in the right direction so I can finish these two. Thanks for your help in advance!
Ok, for the first question when you say : "1. Take the derivative. Set it to 0. Solve for x. Find the cordinates."
I am stuck with the first part. When I take the derivative, what do I put in for "a" in the first principle of derivatives formula? ie. [f(a+h) - f(a)]/h
and then after setting it to 0 and solving for x to find the coordinates.. not sure how to do that part. could you please show me how to begin it and explain more . please and thank you! very much
A strategic move that made my life easier. It is valid because of the theorems on limits says it is.
I first rewrote the quotient as two separate ones by the basic division identity
And since the limit of a sum is the sum of the limits, I could "distribute" the limit to both quotients. (I probably shouldn't use the word distribute, but who cares)