You can use the power rule for derivatives for each problem (though you could also use the product rule for the fourth curve).
y = x ² + 6x - 1 ==> dy/dx = 2x + 6
y = x ² - 5x + 1 ==> dy/dx = 2x - 5
y = 2 - 4x - x ² ==> dy/dx = -4 - 2x
y = (1 + x) (7 - x) = 7 + 6x - x ² ==> dy/dx = 6 - 2x
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or, using the product rule,
dy/dx = (1 + x) (-1) + 1 (7 - x) = -1 - x + 7 - x = 6 - 2x
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Now, stationary points occur where the derivative is zero. We have
2x + 6 = 0 ==> x = -3
2x - 5 = 0 ==> x = 5/2
-4 - 2x = 0 ==> x = -2
6 - 2x = 0 ==> x = 3
