Find the approximate elevation.

A climber on Mt Everest is $6000$ meters from the start of his trail and at elevation $8000$ meters above sea level. At $x$ meters from the start, the elevation is $h(x)$ meters above sea level. If $h^{\text{'}}(x)=0\mathrm{.}7$ for $x$ near $6000$ meters, what is the approximate elevation another $2$ meters along the trail?

Chapter $2,$ Section $2\mathrm{.}3,$ Supplementary Question $001$a

Your answer is correct.

Since the derivative tells how fast a function is changing, use the derivative at a point to estimate values of the function at nearby points. For local linear approximation use$-h=h^{\text{'}}(x)x.$

What are the values for $x$ and $h^{\text{'}}(x)?$

$x=$ meters and $h^{\text{'}}(x)=$

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Attempts: $1$ of $3$ used

Your answer is correct.

Now substitute these values into $h=h^{\text{'}}(x)x.$ What is the value for $h?$

$h=$ meters

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Attempts: $1$ of $3$ used

Chapter $2,$ Section $2\mathrm{.}3,$ Supplementary Question $001$c

Your answer is partially correct.

What does $1\mathrm{.}4$ meters mean in the context of the problem?

The elevation $$ by $1\mathrm{.}4$ meters as the climber moves from $$ to meters along the trail.