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### Section 6-1 : Average Function Value

For problems 1 & 2 determine $${f_{{\rm{avg}}}}$$ for the function on the given interval.

1. $$f\left( x \right) = 8x - 3 + 5{{\bf{e}}^{2 - x}}$$ on $$\left[ {0,2} \right]$$ Solution
2. $$f\left( x \right) = \cos \left( {2x} \right) - \sin \left( {\displaystyle \frac{x}{2}} \right)$$ on $$\displaystyle \left[ { - \frac{\pi }{2},\pi } \right]$$ Solution
3. Find $${f_{{\rm{avg}}}}$$ for $$f\left( x \right) = 4{x^2} - x + 5$$ on $$\left[ { - 2,3} \right]$$ and determine the value(s) of $$c$$ in $$\left[ { - 2,3} \right]$$ for which $$f\left( c \right) = {f_{{\rm{avg}}}}$$. Solution