Use linear approximation, i.e. the tangent line, to approximate $97^4$ as follows:
Let $f(x) = x ^4$. The equation of the tangent line to $f(x)$ at $x = 10^2$ is best written in the form $y = f(a) + f'(a) \cdot (x - a)$ where $a =$ , $f(a) =$ , and $f'(a) =$ .

Using this, we find our approximation: $97 ^4 \approx$ .

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