EMC Q.19

19The maxima and minima of the function f(x) = 2x³ - 15x² + 36x + 10 occur respectively at

Option : C
Explanation : f(x)=2x³-15x²+36x+10 f '(x)=6x²-30x+36 and f ''(x)=12x-30 For maxima and minima, f '(x)=0 6x²-30x+36 = 0 or x²- 5x + 6 = 0 or X = 3,2
Putting these values of x in equation (ii), we get

f '(3) = 36 - 30 = + 6 positive

Hence minimum value = 3

f ' (2) = 24 - 30 = - 6 negative, hence maximum value = 2

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