Example 3 Video Example < Find equations of the tangent line and normal line to the curve y=x√x at the point (9, 27). Illustrate by graphing the curve and these lines. Solution The derivative of f(x) = x√√x = xx¹²/² = x³/2 is f'(x) = So the slope of the tangent line at (9, 27) is f'(9) = ])(x-¯) y- y = y = The normal line is perpendicular to the tangent line, so its slope is the negative reciprocal of or 30 or We graph the curve and its tangent line and normal line in the figure below. 20 10 normal tangent Therefore an equation of the tangent line is 5 10 X 15 e , that is, .Thus the equation of the normal line is

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