The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) dy/dx (ii) d^2y/dx^2 (3 marks) (b) Verify that C has a stationary point when x = 2 (2marks) (c) Determine the nature of this stationary point, giving a reason for your answer. (2)
(a) (i) differentiate C using standard technique: dy/dx = 12x^3 - 24x^2 (ii) to find the second differential differentiate the first derivative (dy/dx): d^2y/dx^2 = 36x^2 - 48x(b) In order to determine if C has a stationary point at x=2 subsitue this value into dy/dx: 12(2)^3 - 24(2)^2 = 0 therefore since dy/dx = 0 C has a stationary point at x=2(c) in order to determine the nature of a stationary point substite x=2 into the secnd differnetial (d^2y/dx^2): 36(2)^2 - 48(2) = 48 48 > 0 therefore the staionary point is a minimum
DP
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