Differentiate. f(x) = ln|ln(4x)| f\'(x) = The body mass index (BMI) is a number

Question

Differentiate. f(x) = ln|ln(4x)| f'(x) = The body mass index (BMI) is a number that can be calculated for any individual by using the equation BMI = 703w/h^2 where weight (w) is in pounds and height (h) is in inches. Use this information to complete the following. Calculate the BMI for a person who weighs 217 pounds and is 6'2'' tall. BMI = (Round to the nearest whole number as needed.) How much weight would the person in have to lose to reach a BMI of 25.2? The person would have to lose pounds. (Round to the nearest whole number as needed.) The body mass index (BMI) is a number that can be calculated for any individual by using the equation BMI = 703w/h^2 where weight (w) is in pounds and height (h) is in inches. Use this information to complete the following. (Round to the nearest whole number as needed.) For a 127-lb. female, what is the rate of change of BMI with respect to height? The rate of change with respect to height is. Calculate f'(64). f'(64) = (Do not round until the final answer. Then round to two decimal places as needed.)

Explanation / Answer

1) f(x) = ln (ln (4x))

f'(x) = 1/ (ln (4x)) *(1/(4x))*4

= 1/ (ln (4x)) *(1/(x))

2) a)   BMI = 703 w /h2

w = 217 pound ,h = 6 ' 2'' = 6*12 + 2 = 74

hence BMI = 703*217/(74)2 =27.858

b) w ,when BMI = 25.2

w = 25.2 *74*74 /703 = 196.294

hence weight to be lost = 217 - 196.294 = 20.706 pound

c) w = 127 pound

we denote BMI by y.

y =  703 w /h2

for w = 127 , y = 703*127/h2  

dy/dh =   703*127 * (-2/ h3) =

= -178562/h3

d) f'(64) = -178562/643 = 0.68115

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