A little lost at how i can tackle the question. any help would be appreciated.
Find the stationary points of the function y=(x^2+1)/x and test them for their nature.
Please show all workings
Find the stationary points of the function y=(x^2+1)/x and test them for their nature.
Please show all workings
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y = x + x⁻¹
y' = 1 - x⁻²
y" = 2x⁻³
y' = 0 when 1 = x⁻²
i.e. x² = 1
x = ±1
When x = 1, y = 2 and y" = 2
hence, since y" > 0,
(1, 2) is a minimum turning point.
When x = -1, y = -2 and y" = -2
hence, since y" < 0,
(-1, -2) is a maximum turning point.
y' = 1 - x⁻²
y" = 2x⁻³
y' = 0 when 1 = x⁻²
i.e. x² = 1
x = ±1
When x = 1, y = 2 and y" = 2
hence, since y" > 0,
(1, 2) is a minimum turning point.
When x = -1, y = -2 and y" = -2
hence, since y" < 0,
(-1, -2) is a maximum turning point.