Question

Find the points of the graph of y= x^2 + 4ln(x) at which the tangent line is parallel to the line y= 6x - 3.

Thanks!

Answer 1

the solpe of the tangent must be equal to the slope of the line which is 6

Answer 2

here dy/dx =2x + 4/x
by the problem
2x +4/x =6
or x+2/x=3
2=(3-x)x
or x^2 -3x+2=0
or (x-1)(x-2)=0
thus x=1,2
thus at x=1 or 2 tangent to the given curve is parallel to the given line
when x=1 y = 1+4ln1=1
when x=2 y=4+4ln2

thus the reqd pts are (1,1) and (2,4+4ln2)