Write the equation of a tangent line given an x value.

Question

How do I find the equation of a line tangent to y=Square root (x-4) when the x =5.

I used point slope form and got the y1 value but I can’t find the slope.

Answer 1

Let find tangent point: x = 5, y = sqrt(5 - 4) = 1; tangent point is (5, 1).

Derivative y' = 1/2·(x - 4)^-1/2 ; slope m of tangent line at point (5, 1): m = 1/2(5 - 4)^-1/2 = 1/2.

Using point-slope equation we get: y - 1 = 1/2·(x - 5), y = 1/2·x - 5/2 + 1;

y = 1/2·x - 3/2.

Answer: equation of tangent line is y = 1/2x - 3/2