Question

find an equation of the tangent line to the curve of y= xsqrt(x) that is parallel to the line y= 1+3x

Answer 1

y= xsqrt(x)


y'= sqrt(x)+x/(2*sqrt(x))


Since you want the tangent line to be parallel to 1+3x, this means that the slope of the tangent line is 3, so y'(x) = 3


This means that

3 = sqrt(x)+x/(2*sqrt(x))


From here, solve the equation to find the value of x where this tangent touches the graph of y. Once you have x, you can find y and the equation of the tangent line.