Derivative Practice – Numbers

Here is an example of how to help your students practice their derivative rules in a different way.  Tomorrow another different approach.
Let f be a differentiable function. The table below gives values of f and g their first derivatives at selected values of x

x   -2    0   2   4   6
 f\left( x \right) -8 0 –2 2 5
 {f}'\left( x \right)  2  4 –3 –1 0
 g\left( x \right) 2 4 5 6 5
 {g}'\left( x \right) 1 2 4 3  2
    1. If h\left( x \right)=f\left( x \right)+3g\left( x \right) find  {h}'\left( 2 \right)
    2. If \displaystyle j\left( x \right)=\frac{f\left( x \right)}{g\left( x \right)} find  {j}'\left( 4 \right)
    3. If  r\left( x \right)=f\left( g\left( x \right) \right)  find  {r}'\left( 0 \right)
    4. If  s\left( x \right)=g\left( f\left( x \right) \right)  find  {s}'\left( 2 \right)
    5. If  q\left( x \right)=g\left( x \right)f\left( x \right) find  {q}'\left( -2 \right)
    6. Approximate  {g}'\left( 3 \right)
    7. Write an equation of the line tangent to g at the at the point where = 0.

Answers:

1. 9,     2. -1/3,     3. -2,     4. -3,     5. -5,     6. 1/2,    7.  y=4+2(x-0) or y = 4+2

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