SOLUTION: A right triangle is formed in the 1st quadrant. It has vertices at A(0,0), B(0,y), and C(x,y). Point C is on the graph of the function f(x)=8+x-x^4. Write an equation to show how t

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: A right triangle is formed in the 1st quadrant. It has vertices at A(0,0), B(0,y), and C(x,y). Point C is on the graph of the function f(x)=8+x-x^4. Write an equation to show how t      Log On

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Question 175227: A right triangle is formed in the 1st quadrant. It has vertices at A(0,0), B(0,y), and C(x,y). Point C is on the graph of the function f(x)=8+x-x^4. Write an equation to show how the triangle area varies with x and find the maximum area.
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The area of the triangle is the base times the height divided by 2, or xy%2F2, so the Area function is A%28x%29=%288x+%2B+x%5E2+-+x%5E5%29%2F2. The first derivitive of the Area function: dA%28x%29%2Fdx=8+%2B+2x+-+5x%5E4, set equal to zero will yield the x coordinate of the extreme point.