Find the point on the curve `y=4x-x^2` where the tangent is parallel to the x-axis.

Explanation

Given curve is `y=4x-x^2`
`therefore dy/dx=4-2x`
Since, the tangent is parallel to the x-axis, so we have,
dy/dx=0
`implies 4-2x=0impliesx=2`
Putting x=2 in the given curve, we have,
`y=4.2-2^2=4`
Hence, at (2,4) the given curve is parallel to the x-axis.