2.1.3-eg-1 - f x = tan x-x over the interval-π 4,π 4 is...

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Example Find the average rate of change of the function f ( x ) = tan x - x over the interval [ - π/ 4 ,π/ 4]. Solution: The average rate of change of a function f ( x ) over the interval [ a,b ] is given by the slope of the secant line joining ( a, ( f ( a )) to ( b,f ( b )), or by f ( b ) - f ( a ) b - a . So the average rate of change of
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Unformatted text preview: f ( x ) = tan x-x over the interval [-π/ 4 ,π/ 4] is given by f ( π/ 4)-f (-π/ 4) π/ 4-(-π/ 4) = (tan( π/ 4)-π/ 4)-(tan(-π/ 4)-(-π/ 4)) π/ 2 = 2 π ±² 1-π 4 ³-²-1 + π 4 ³´ = 2 π ² 2-π 2 ³ ....
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