A differentiable error function is used to assess how well a parameter models the…

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A differentiable error function

E(k)

is used to assess how well a parameter

k

models the drag force on a drone. It is known that •

E(k)>0

for all

k>0

; •

E'(k)<0

(0,2)

E'(2)=0

, and

E'(k)>0

(2,\infty)

; •

E''(k)=3k+1

for all

k>0

. (a) Describe what the sign pattern of

E'(k)

indicates about the behavior of

E(k)

(0,\infty)

. (b) Justify that

k=2

yields the minimum possible error, citing appropriate analytical evidence. (c) Explain the role of the second derivative in confirming that

k=2

corresponds to a minimum rather than a maximum or point of inflection.