2 years ago

A division word problem that can be represented by 4/3

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Here are some examples of division word problems that can be solved in two steps. We will illustrate how block diagrams or tape diagrams can be used to help you to visualize the division word problems in terms of the information given and the data that needs to be found. We also learn how to solve multiplication and division word problems by identifying key terms.

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Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

slavikrds [6]

$f'(x)=2x-\dfrac3{x^4}$
$\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx$
$f(x)=x^2+\dfrac1{x^3}+C$

Given that $f(1)=2$ , we get

$2=1^2+\dfrac1{1^3}+C$
$2=2+C$
$\implies C=2$

so that

$f(x)=x^2+\dfrac1{x^3}$