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Extrema
How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.
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Given the function \(f(x)=3x^3-9x^2+14x+36,\) what is the inflection point \((a,b)\) of \(f(x)\)?
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If one of the inflection points of the curve \[ y = \ln (ax^2 + b) \] is \( (1, \ln 50) \), what is the value of \( a \times b \)?
Excel in math and science
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Let \(f(x)=x^3+12x^2+3x-5.\) If \(a\) and \(b\) are constants such that the inflection point of the curve \(y=f(x-a)+b\) is the origin \( (0,0),\) what is the ordered pair \((a,b)?\)
Excel in math and science
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If \(a\) and \(b\) are constants such that the curve \[f(x)=\ln (ax^2 + b)\] has an inflection point \((1,\ln 16),\) what is the value of \(ab?\)
Excel in math and science
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The slope of the tangent line to the curve \[y=ax^3-bx^2+cx\] at \(x=2\) is \(13,\) where \(a, b\) and \(c\) are constants. If \(P=(1,7)\) is the inflection point of the curve, what is the value of \(a+b+c\)?
Excel in math and science
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