Find the exact coordinates of the point on the curve y =x /1 + ln(x) at which the gradient of the tangent is equal to 1/4.

0 < x < 1

Step-by-step explanation:

the derivative of the curve allows one to compute the slope:

(1/1-x) is the value of the slope, which depends of the point x. By using the line equation we have:

where yl is the tangent line of the original curve y in the point x.

For the intersection point (0,2), with b=2, we obtain:

The denominator must be different of zero. And the original curve y(x) only can take values of x < 1. Hence the positive value of x for the tangent line will be:

0 < x < 1

hope this helps!!