Question: Challenge: Consider the function f(x)=11-x.In first semester cal-culus you learn how to find the equation of the tangent line to thisfunction at the point (0,1).

Challenge: Consider the function f(x)=11-x.In first semester cal-culus you learn how to find the equation of the tangent line to thisfunction at the point (0,1). You used the fact that the tangent line hasthe same value and the same slope as the function when x=0. Our goal here isto find a tangent polynomial. Letp(x)=ax4+bx3+cx2+dx+e,i.e. a fourth degree polynomial. Find the numbers a,b,c,d,e such that(a)f(0)=p(0),(b)f'(0)=p'(0),(c)f''(0)=p''(0),(d)f'''(0)=p'''(0), and(e)f'''''(0)=p''''(0).Does this polynomial bear any resemblance to a familiar type of series?

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