Use linear approximation, i.e. the tangent line, to approximate 999^4 as follows:
Let f(x)=x^4. The equation of the tangent line to f(x) at x=10^3 is best written in the form y=f(a)+f'(a)*(x−a) where a=10^3, f(a)=(10^3)^4, and f'(a)=4(10^3)^3.
Using this, we find our approximation: 999^4 approximately equals? ______
I'm stuck at the last part and can't figure it out. Can someone walk me through it without giving me the answer?

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OOOHHH!! So I plug 999^4 into x in the equation!

You probably made a miscalculation for f'(a)=4(10^3)^3 with a ^3 too many.

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