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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.
Source: Mandelbrot #2
by
Daniel Liu
If \(S = \dfrac{a\sqrt{b}}{c},\) where \(a,c\) are positive coprime integers and \(b\) is a positive square-free integer, find \(a + b + c.\)
by
Brian Charlesworth
How many real values of \(x\) satisfy the equation
\[\large {x}^{2}-{2}^{x}=0? \]
by
Michael Fuller
Suppose that two people, A and B, walk along the parabola \(y=x^2 \) in such a way that the line segment \( L\) between them is always perpendicular to the line tangent to the parabola at A's position \((a,a^2)\) with \( a > 0 \). If B's position is \((b,b^2)\), what value of \(b\) minimizes \(L\)?
by
Jared Jones
Note : The picture shown is a rough one.
by
Sandeep Bhardwaj