Consider the function on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the function f(x)=x2+3x+2f(x)=x^{2}+3x+2 on the interval [1,4][1,4]. (i) Calculate the average value fˉ\bar f of ff on [1,4][1,4]. (ii) Find all real numbers cc in (1,4)(1,4) that satisfy f(c)=fˉf(c)=\bar f. Show each step of your working.

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