The line y=2x+b is tangent to the graph of y=x^1/2 at the point P=(a, a^1/2). Find P and determine b.

Question

I don't know what to do because they don't give you the x coordinate or anything to plug into the derivative. Help?

Answer 1

y=sqrt x

y'=1/(2sqrtx)

but y=2x+b, slope is 2, so
2=1/(2sqrtx)

sqrt x=1/4

x=+ 1/2

solve for y.

Answer 2

thank you soo much!