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(Solved): A right triangle has one vertex on the graph of y=x3 at the point (x,y) in the first quadrant, anot ...
A right triangle has one vertex on the graph of at the point in the first quadrant, another at the origin, and the third on the positive -axis at the point , as shown in the figure below. a) Express , the area of the triangle, as a function of . State the natural domain of . b) What is the area of this triangle when ? c) Explain why this area cannot be maximized.
Expert Answer
(a) We know that, Area of right triangle = So, Area of the given right triangle = Since, So, Area of the given right triangle = A(x) = Therefore, Area of the given right triangle is found in terms of x. Now, we have to determine the natural domain of A = A(x) . Since, we can put any value the above function. So, the natural domain of A = A(x) is: The area and natural domain is calculated using required formula and concepts.