The approximate value of (3.978)^{3/2} is | vedclass

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(C) Let $f(x) = x^{3/2}$.Then,$f'(x) = \frac{3}{2} x^{1/2}$.We can write $3.978$ as $a + h$,where $a = 4$ and $h = -0.022$.Using the linear approximat

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$7.934$

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(C) Let $f(x) = x^{3/2}$.Then,$f'(x) = \frac{3}{2} x^{1/2}$.We can write $3.978$ as $a + h$,where $a = 4$ and $h = -0.022$.Using the linear approximation formula $f(a + h) \approx f(a) + h \cdot f'(a)$:$f(4) = 4^{3/2} = 8$.$f'(4) = \frac{3}{2} \cdot (4)^{1/2} = \frac{3}{2} \cdot 2 = 3$.Therefore,$f(3.978) \approx 8 + (-0.022) \cdot 3$.$f(3.978) \approx 8 - 0.066$.$f(3.978) \approx 7.934$.

The approximate value of $(3.978)^{3/2}$ is

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