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# Differentiability

Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.

Let \(\alpha,\beta,\gamma\) be the roots of the equation above.

Evaluate \(\left\lfloor \alpha \right\rfloor +\left\lfloor \beta \right\rfloor +\left\lfloor \gamma \right\rfloor \).

Let \(f\) be a twice differentiable function satisfying \(f(1)=1, f(2)=4, f(3)=9\), then :

Find the equation of common tangent to the curves \(y^2=8x\) and \(xy=-1\)?

The curve of \(\sin { \left( ax \right) } \) is tangent to the curve of \(\sin { \left( x \right) } \) at \(x=\frac { 5\pi }{2 } \).

If minimum positive value of \(a\) can be expressed as \(\frac { A }{B }\) for co-prime \(A\) and \(B\), then find \(A+B\).

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