Section 6.1 : Average Function Value
For problems 1 & 2 determine \({f_{{\rm{avg}}}}\) for the function on the given interval.
- \(f\left( x \right) = 8x - 3 + 5{{\bf{e}}^{2 - x}}\) on \(\left[ {0,2} \right]\) Solution
- \(f\left( x \right) = \cos \left( {2x} \right) - \sin \left( {\displaystyle \frac{x}{2}} \right)\) on \(\displaystyle \left[ { - \frac{\pi }{2},\pi } \right]\) Solution
- 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