Question: Use linear approximation, i.e. the tangent line, to approximate 6.7^3 as follows: Let f(x)=x^3. The equation of the tangent line to f(x) at x=7 can

Use linear approximation, i.e. the tangent line, to approximate 6.7^3 as follows:

Let f(x)=x^3. The equation of the tangent line to f(x) at x=7 can be written in the form y=mx+b

where m is:

and where b is:

Using this, we find our approximation for 6.7^3 is

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