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Unformatted text preview: r answers graphically using a calculator.
1. x2/3 < x4/3 − 6
2. 3(2 − x)1/3 ≤ x(2 − x)−2/3
9 The proper Calculus term for this is ‘vertical tangent’, but for now we’ll be okay calling it ‘unusual steepness’.
See page 185 for the ﬁrst reference to this feature. 5.3 Other Algebraic Functions 317 Solution.
1. To solve x2/3 < x4/3 − 6, we get 0 on one side and attempt to solve x4/3 − x2/3 − 6 > 0. We
set r(x) = x4/3 − x2/3 − 6 and note that since the denominators in the exponents are 3, they
correspond to cube roots, which means the domain of r is (−∞, ∞). To ﬁnd the zeros for
the sign diagram, we set r(x) = 0 and attempt to solve x4/3 − x2/3 − 6 = 0. At this point,
it may be unclear how to proceed. We could always try as a last resort converting back to
radical notation, but in this case we can take a cue from Example 3.3.4. Since there are
three terms, and the exponent on one of the variable terms, x4/3 , is exactly twice that of the
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