The equation of the tangent line to f(x) =sqrt{x} at x = 25 can be written in the form y = mx+b

Question

where m =.1
b =?
i don't know how to find the value of b

Answer 1

y = sqrt x = x^(1/2)
dy/dx = (1/2) x^-1/2)
at x = 25
dy/dx = slope = m = (1/2)/5 = 1/10
so
y = .1 x + b
when x = 25, y = 5 so the line goes through (25,5)
5 = .1 (25) = b
5 = 2.5 + b
b = 2.5
so
y = .1 x + 2.5

Answer 2

thank you