Question

1. The maximum and minimum values of the function y = x - 3x + 6 are
(2) 6, 0
(1) 2.0
(4) 4,2
(3) 6, 2
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Answer 1

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The maximum and minimum values of the function y=x³-3x²+6

The maximum and minimum values of the function y=x³-3x²+6

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A)

y= x^3-3x^2+6

dy/dx = 3x^2 - 6x

d^2y/dx^2 = 6x - 6

To find the maximum and minimum values, put dy/dx = 0

3x^2 - 6x = 0

3x(x-2) = 0, this implies x =0 and x=2

when x=0, y= 6 and x = 2, y = 2

Hence the maximum value is 6 and minimum value is 2