Question

Use the fact that the derivative of the function g(x) = /x is g'(x) = 2/x to find the equation of the tangent line to the graph of g(x) at the point x = 1. %3D The equation of the tangent line is y = (Simplify your answer.)

Answer 1

given 9'la)= 9la)= G, y: 9la) y(1)= y=1} (!,;) 7, Y, hence has Coordinates Poinl- that dy -) given dx Slope is The tangent of where m: 9'(x) 2(x we hove (', !) The equation of the tongent m (x- 2,) 9-4, = y -1 aly-1) = dy - 2 : x - ay +1=0

given f'x ) : 1: -9 F(a) = Setting Jet -) in given funt hion we 9- Coordinate y. f{-9) (-9, The • Coodinate Point is y, is The -the tangent Slope m: f(a) (-१, ३) hove we - 5 81 eguahion The of fangent is 4-4,= m (7- 7,) y-l2): -5 (x-49)) 8i y + 81) - 5x - 5 81 y + u5 :: -5x - u5 6x.+ 81y + 90=0

Qy= y= 5 x+ 81y +90=0 81y -5x~90 = - 5x- 90 81 -5