2.3 Lösning 5a

\( f(25+h) = 4\,(25+h)^2 - 380\,(25+h) + 9000 = \)

\( = 4\,(625+50\,h+h^2) - 9500 - 380\,h + 9000 = \)

\( = 2500 + 200\,h + 4\,h^2 - 500 - 380\,h = \)

\( = 4\,h^2 - 180\,h + 2000 \)

\( f(25) = 4\cdot 25^2 - 380\cdot 25 + 9\,000 = 4\cdot 625 - 9500 + 9000 = 2000 \)

\( {\Delta y \over \Delta x} = {f(25+h) - f(25) \over h} = {4\,h^2 - 180\,h + 2000 -2000 \over h} = {4\,h^2 - 180\,h \over h} = \)

\( = {h\cdot (4\,h - 180) \over h} = 4\,h - 180 \)