At the National Council of Teachers of Mathematics (NCTM) illuminations website, students are encouraged to collect data on howmany drops are required to break a blanched peanut in two pieces. The data can be modeled by the function88f(h) = 0.8 +ñ-10where h is the height in centimeters. Suppose that the peanut hummingbird collects peanuts and wants to minimize the amount of workrequired to break a peanut into two halves. Determine the height which minimizes the amount of work to break open the peanuts.cm.How many drops needed(decimal number OK, try not to round off)?drops.

Given, f(h)=0.8 + 88h-10 The total Distance need to be travelled by the bird = D = 2 × height × Number of drops = 2 ×h×0.8+88(h-10) = 1.6h + 176h(h-10) For minimising the Distance,dDdh=0 ⇒1.6+176(1)(h-10)-(1)(h)(h-10)2=0⇒1.6+ 176-10(h-10)2=0⇒1.6-1760(h-10)2=0⇒1760(h-10)2=1.6 ⇒1100=(h-10)2 ⇒(h-10)=33.166 ⇒h=10+33.166 ⇒h=43.166 So, the height which minimises the amount of work to break open their peanuts is 43.166 cm Number of drops = f(h) =( 0.8+88h-10) for h=43.166 cm , ⇒f(h) = number of drops = 0.8+(8843.166-10) =0.8+2.6533= 3.4533 drops So 3.4533 drops are needed.