Anonymous's answer is completely correct. I thought this problem was asking how to find the distance along the function from the point (2,2^8), and wrote the answer to that nice, tasty problem.
Simply integrate the line element with respect to some affine parameter!
<span><span>L=<span>∫10</span><span><span><span><span>(<span><span>∂x</span><span>∂λ</span></span>)</span>2</span>+<span><span>(<span><span>∂y</span><span>∂λ</span></span>)</span>2</span></span><span>−−−−−−−−−−−−−</span>√</span>dλ</span><span>L=<span>∫01</span><span><span><span>(<span><span>∂x</span><span>∂λ</span></span>)</span>2</span>+<span><span>(<span><span>∂y</span><span>∂λ</span></span>)</span>2</span></span>dλ</span></span>
In this case,
<span><span>x(λ)=λ(X−2)+2,</span><span>x(λ)=λ(X−2)+2,</span></span>
<span><span>y(λ)=(λ(X−2)+2<span>)8</span>.</span><span>y(λ)=(λ(X−2)+2<span>)8</span>.</span></span>
<span>Note that this approach can also solve the original problem, with some simplification.</span>
The value of f(x) when x=6 is A 27
