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To find stationary points, we need to find dy/dx and set it equal to 0. Here we must use implicit differentiation: d/dx(x²) + d/dx(-xy) + d/dx(y²) = d/dx(12). Hence 2x - x(dy/dx) - y...

f(x) = x³ + 2x² - x - 2 Use the factor theorem to test for f(1) = 0 f(1) = 1³ + 2*1² - 1 - 2 = 0 Therefore x = 1 is a solution and (x-1) is a factor of f(x) Now...

Differentiation dy/dx = 2+12x^2+12x^3
Chain ruleu = 1+xz=u^2dz/dx = dz/du * du/dx = 2u * 1 = 2(1+x)

5x -2y = 33 (substract) 5x + 8y = 18
-10y = 15
y = -1.5
5x + 8(-1.5) = 18
5x = 30
x= 6