Question bank/JEE Main/Mathematics

Number of point of minima of the polynomial
$y = 10x^{6} - 24x^{5} + 15x^{4} - 40x^{2} + 108$ is (are) equal to ?

A1B2C3D4

Show answer and solution▾

$\frac{dy}{dx} = 60x^{5} - 120x^{4} + 60x^{3} - 80x$
$= 20x(3x^{4} - 6x^{3} + 3x^{2} - 4) = 0$
$g(x) = 3x^{4} - 6x^{3} + 3x^{2} - 4$
$g^{'}(x) = 12x^{3} - 18x^{2} + 6x = 0$
[IMAGE] g(x) have two zeros on less than zero and other greater than zero
Hence given function will have two point of minima and one point of
maxima.

Source: Grass-G / M-12 Mathematics Paper 2 Nov.docx