Hi, I am trying to figure out how to find the maxima and minima of the function f(x)=(x^3-10*x^2-2*x+1)/(4*x^3+5*x+1) and its derivative.

a) Find the local maxima and minima of f. 

b) Find the vertical asymptote

I graphed the function and located the  local max to be (-1,1) and local min (1,-1) however, I can't figure out how to plot the derivative of the function. I tried to use the diff expression but it leaves the graph empty when i attempt to plot it.

Also, just curious how am i able to join text words and maple commands together? For example, I want to be able to say "The derivative of the original function is [maple command here]" ? I tried to switch from text to math however nothing worked.

Thanks in advance!

Hi, I am stumped I've tried many ways but end up getting a graph with nothing on it or errors. I am trying to plot the tangent line to the equation f(x) = 2cosx-x^2 at x = 2; In addition, how would I plot the tangent line and the equation on one graph with distinctive line pattern for example, one being blue and dotted, while the other being red solid).

Thanks in advance!