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Excel in math and science
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Calculus
Extrema
Excel in math and science
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Let \(P\) and \(Q\) be the two inflection points of the curve \(\displaystyle y=e^{-5x^2}.\) What is the area of the triangle \(OPQ,\) where \(O\) is the origin?
Excel in math and science
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If \(\displaystyle{f(x)=\frac{1}{x^2+9}},\) the interval on which the curve \(y=f(x)\) is concave down can be expressed as \(a<x<b.\) What is the value of \(ab?\)
Excel in math and science
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Let \(\displaystyle{f(x)=8+\frac{a}{x}+\frac{b}{x^2},}\) where \(a\) and \(b\) are constants. If the point \((-1,0)\) is the inflection point of the curve \(y=f(x),\) what is \(a+b?\)
Excel in math and science
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If \( f(x) = x^{1/3}(x + 26) \), the interval on which the curve \( y = f(x) \) is concave down can be expressed as \( a < x < b \). What is the value of \( a + b \)?
Excel in math and science
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Let \(y=(ax^2+30)e^x\) be the equation of a curve, where \(a\) is a constant. If \(A\) and \(B\) are two distinct arbitrary points on the curve and the arc between the two points always lies below the line connecting the two points, what is the range of \(a?\)
Excel in math and science
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Our wiki is made for math and science
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by Brilliant Staff