Find the equation of the tangent line and normal line to the curve y=x sqrt x at the point (16,64).

webassign.net/web/Student/Assignment-Responses/last?dep=27538054 Update 1. [-/2 Points] DETAILS SCALCET8 3.1.AE.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER SO EXAMPLE 3 Find the equations of the tangent line and normal line to the curve y = xv x at the point (16, 64). Illustrate the curve and these lines. normal SOLUTION The derivative of ((x) = xV x = xx1/2 =. x3/2 Is 60 f'(x) = 3/2 x( 3/2 -1 X 1/2 3Vx 2 20 So the slope of the tangent line at (16, 64) Is f'(16) - Therefore an equation of the tangent line is tangent or 5 10 15 20 Video Example ) 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 - 64 16 Enter an exact number. or We graph the curve and its tangent line and normal line In the figure to the left. Need Help? Read It