Calculus- find the value c such that the y=3/4x + 3 is tangent to the curve f(x)=csqrtofX

Answer 1

y1=cx^1/2

y1'=(1/2)cx^-1/2

y2=(3/4)x+3

y2'=-3/4

c=(3/2)x^1/2

that is condition for same slope

now, set values of functions equal

cx^1/2=(3/4)x+3

c=(3/4)x^1/2+3x^-1/2

set c=c

3/2=3/4+3x^-1

x=4

in slope equation c=(3/2)x^1/2

c=3