use the definition of the derivative to calculate f'(x), if f(x)= SQRT(2x) and find the equations of the tangent line and the normal line to the graph of f at x=2

Answer 1

f(x) = √(2x)
f '(x) = (/2)(2)(2x)^(-1/2) or 1/√(2x)

f(2) = 2
f'(2) = 1/2

tangent equation:
x - 2y = c
at (2,2)
2-4=c
c = -2

tanglent: x-2y=-2

normal: slope = -2
equation:
2x + y = k
at (2,2,)
4+2 = k = 6

normal : 2x + y = 6