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 x = 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+2x

4 thoughts on “Derivative Practice – Numbers”

kaleb40 on October 18, 2012 at 10:27 said:

How can you find the tangent to g at the origin, when it doesn’t go through the origin?

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- Lin McMullin on October 18, 2012 at 13:39 said:
  
  Whoops again. See reworded question.
  
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reremake on October 16, 2012 at 17:26 said:

Hi. Can you help me with #5? How is it q(x)? I’m confused. Thanks.

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- Lin McMullin on October 16, 2012 at 19:23 said:
  
  My mistake. Thanks for catching this. I have corrected the answer to #5
  
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Derivative Practice – Numbers

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