Find equations of the tangent line and normal line to the curve y = xv x at the point (4, 8). Illustrate by graphing the curve and these lines. Solution The derivative of f(x) = XV x = xx1 /2 = x3/2 is F' ( x) = ( 0 )( 0-1) -(0)0 So the slope of the tangent line at (4, 8) is f'(4) = Therefore an equation of the tangent line is y - or y The normal line is perpendicular to the tangent line, so its slope is the negative reciprocal of , that is, Thus the equation of the normal line is y - = or Y =