Find the Domain V=x(14-2x)(14-2x)

Problem

V=x*(14−2*x)*(14−2*x)

Solution

1. Identify the context of the expression, which represents the volume of a box formed by cutting squares of side length x from the corners of a 14×14 sheet.

2. Set constraints for the side length x which must be a positive value.

x>0

3. Set constraints for the resulting dimensions of the base, (14−2*x) which must also be positive to form a physical object.

14−2*x>0

4. Solve the inequality for x by subtracting 14 from both sides.

−2*x>−14

5. Divide by −2 and reverse the inequality sign.

x<7

6. Combine the inequalities to determine the interval of valid x values.

0<x<7

Final Answer

Domain:(0,7)

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