The quantity models the mass of a culture (in grams) after hours

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The quantity

f(x)=(x^{2}+4)^{\sqrt{x}}

models the mass of a culture (in grams) after

x

hours, with

x>0

. What is the instantaneous percent rate of change of

f

at

x=4

? (Percent rate of change is defined as

100\cdot\dfrac{f'(x)}{f(x)}

.) (a)

100\left(\dfrac{1}{4}\ln 20+1\right)\%

(b)

100\left(\dfrac{1}{4}\ln 20\right)\%

(c)

100\left(\dfrac{1}{4}\ln 20+\dfrac{4}{5}\right)\%

(d)

100\left(\dfrac{1}{2}\ln 20+\dfrac{4}{5}\right)\%

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