Here are my answers
x = 3 mine agrees with yours
x = 3.5 m = [1/2 - 1/sqrt(3.5)] / [4 - 3.5 ] = -.0690
x = 3.75 m = [1/2 - 1/sqrt(3.75)] / [ 4 - 3.75] = -.0656
x = 3.9 m = [1/2 - 1/sqrt(3.9)] / [ 4 - 3.9] = -.0637
x = 3.95 m = [1/2 - 1/sqrt(3.95)] / [ 4 - 3.95] = -.0631
x = 3.99 m = [1/2 - 1/sqrt(3.99)] / [ 4 - 3.99] = -.0626
It appears that as x → 4, the slope is about -.0626
If you haven't had Calculus.....hide your eyes......but the exact slope at x = 4 is given by :
(-1/2)(x)-3/2 = (-1/2)(4)-3/2 = -.0625
The equation of the tangent line is given by :
y - (1/2) = -.0625(x - 4)
y = -,0625x + 1/4 + 1/2
y = -.0625x + 3/4
Here's a graph of the function and the tangent line.....https://www.desmos.com/calculator/ygyhq8trhm
