1. The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) d d y x (ii) d d 2 y x 2 (3) (b) Verify that C has a stationary point when x = 2 (2) (c) Determine the nature of this stationary point, giving a reason for your answer.
To differentiate use formula.
multiply factor by power then minus one from power (where x is invloved)
dy/dx = 12x^3 - 24x^2
d^2y/dx^2 = 36x^2 - 48x (this is just a further differentiation)
b) to find stationary point, put value of x into gradient equation (dy/dx) and it should equal to zero (hence stationary)
c) put value of x into second derivative. answer = 48 = positive hence the nature of this point is positive
EI
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