MATH 2301-102 Fall 2018 Calculus I Recitation 2 Week 3

See the coversheet for instructions and the point value of each problem.

  1. Let \(f(x)=\sqrt{x}-2\).
    1. State the definition of the derivative as a limit.
    2. Using this definition, compute \(f'(x)\).
    3. Find the equation for the tangent line at \(x=9\).
    4. Graph \(f(x)\) and the tangent line.
  2. For \(f(x)= (2x+1)^{-1}\), compute \( \displaystyle\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=\)
  3. The graph of a function \(f\) is given in each part below. Copy this graph and then sketch the graph of \(f'\) on the same axes.
  4. Sketch the graph of a function \(g\) for which \(g(0)=g'(0)=0\), \(g'(-1)=-1\), \(g'(1)=3\), and \(g'(2)=1\).

Last modified: Fri Sep 7 14:44:31 UTC 2018