the weight w of a man can be known from his height h by the relation w = 5h^2+2h where w is in grams and h in centimeters. The error in measuring his height is 0.3 cm.
Calculate the approximate error in weight when his height is measured to be 168 cm.

Question

the weight w of a man can be known from his height h by the relation w = 5h^2+2h where w is in grams and h in centimeters. The error in measuring his height is 0.3 cm.
Calculate the approximate error in weight when his height is measured to be 168 cm.

queelius · Answer

Two general approaches. The first approach is to just solve: max{|w(h+e)-w(h)|,|w(h-e)-w(h)|}. This gives 5e^2+2e(5h+1). Let h=168 and e=0.3, and you have your answer.

The solution they are more likely interested in is based on calculus. First, what is the rate of change of w with respect to h? 10h+2. Now, construct a linear approximation of the function, w(h), near h*: w(h) ~ w(h*) + w'(h*)(h-h*). We are given that |h-h*|=0.3, and h*=168. We only care about the output of w'(h*)(h-h*)... So, the solution is:

w'(168)(0.3)

anonymous · Answer

is w' = dw/dh ?  the answer given is 504.6 grams @queelius

queelius · Answer

Yes, w' is dw/dh, I apologize for not making that clearer.

(10(168)+2)(3/10)=3*168+6/10=504.6

anonymous · Answer

could anyone explain it a little more clearly??

anonymous · Answer

i don't understand how the error is propagating from h to w

anonymous · Answer

the weight equation is quadratic so simple h error will result in a quadratic weight error...