Given expression is
[tex]y= 6x -x^2[/tex]
And we have to find the slope of the tangent line at the point (1,5), and for that, first we find the derivative of the given expression, which is
[tex]dy/dx = 6-2x[/tex]
And the derivative is the slope. And to find the slope at point (1,5), we put 1 for x in the expression of derivative, that is
[tex]dy/dx = 6-2(1) = 4[/tex]
Hence, the slope of the tangent line to the parabola at the point (1, 5) is 4.
