Derivative Practice – Graphs

Another way to practice the derivative rules.

The graph below shows two piecewise defined functions, f and g, each consisting of two line segments.

  1. If h\left( x \right)=2g\left( x \right)-5f\left( x \right) calculate {h}'\left( 3 \right)
  2. If j\left( x \right)=f\left( x \right)g\left( x \right) calculate {j}'\left( -4 \right)
  3. If k\left( x \right)={{x}^{2}}f\left( x \right) calculate {k}'\left( 5 \right)
  4. If  r\left( x \right)=f\left( g\left( x \right) \right)  calculate {r}'\left( 0 \right)
  5. Write the equation of the line tangent to the graph of y=2+f\left( x \right)g\left( x \right) at the point  \left( -4,2 \right).

There are a lot more like these that you can ask from the same graph; or make up your own graph and questions.

Answers:  1. -17/3,     2. 6,     3.  75,     4. -1/3,     5. y = 2 + 6(x + 4)   (Corrected 10-3-12 19:10)


3 thoughts on “Derivative Practice – Graphs

  1. Pingback: Seeing the Chain Rule | MATHMANMCQ

  2. Hi Lin,
    Thank you for posting this and the derivatives of tabular functions. We used the graphing one today in class and I think there are a couple of typos. I think for number 1 you mean h'(3) and the answer would be -17/3?


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