$\"\"$

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The equation is $\"\"$ .

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Rewrite the equation.

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$\"\"$ .

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$\"\"$ .

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(a) Graph:

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Graph the function $\"\"$ .

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$\"\"$

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$\"\"$

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(b) Evaluate the integral to find $\"\"$ in terms of $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ , where $\"\"$ .

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Let us consider $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Graph:

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Graph the function $\"\"$ .

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$\"\"$

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$\"\"$

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(c)

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The equation is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The slope of $\"\"$ is $\"\"$ .

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The equation is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The product of two slopes is $\"\"$

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$\"\"$ .

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Therefore, the two tangents to the two graphs are perpendicular at points of intersection.

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$\"\"$

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(a)

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Graph of the function $\"\"$ is

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$\"\"$

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(b)

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The equation is $\"\"$ .

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Graph of th function: $\"\"$ .

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$\"\"$

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(c) The tangents to the graphs are perpendicular at points of intersection.