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TextLocal Maxima and Local MinimaDerivative of Implicit Functions2 sub-questions

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Show that the function f(x) = 4x³ – 18x² + 27x – 7 has neither maxima nor 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).

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Local Maxima and Local Minima

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Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h. The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as F = V²/500 – V/4 + 14. On the basis of the above information, answer the following questions :

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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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The perimeter of a rectangular metallic sheet is 300 cm. It is rolled along one of its sides to form a cylinder. Find the dimensions of the rectangular sheet so that volume of cylinder so formed is maximum.

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MCQ (Single)Local Maxima and Local MinimaFirst Derivative Test for Maxima and Minima