Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

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TextMaximum and Minimum Values of a FunctionFirst Derivative Test for Maxima and Minima

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If M and m denote the local maximum and local minimum values of the function f(x) = x + 1/x (x ≠ 0) respectively, find the value of (M – m).

TextLocal Maxima and Local MinimaFirst Derivative Test for Maxima and Minima

It is given that function f(x) = x⁴ – 62x² + ax + 9 attains local maximum value at x = 1. Find the value of 'a', hence obtain all other points where the given function f(x) attains local maximum or local minimum values.

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