Question

Find the point on the curve y = gent line is parallel to the line y = x
√ y = x to y = x
x where the tan-8 .
(b) On the same axes, plot the curve y = √
√ x, the line
8 , and the tangent line to y = x that is parallel 8 .

Answer 1

proofread your post and fix it, ok?
also, not sure how to interpret

y = x
√ y = x to y = x

and what is "tan-8"? tan^{^-1}8 ?

For (b), I'll guess you want
where the tangent line to y=√x is parallel to y=x
If so, then since the slope of y=x is 1,
y' = 1/(2√x)
so
1/(2√x) = 1 at x = 1/4
that would be at the point (1/4, 1/2)
see

www.wolframalpha.com/input?i=plot+y%3D%E2%88%9Ax%2C+y%3Dx%2B1%2F4