The function f (x) = x2-x + alnx is known to have the extremum at x = 32. (1) find the tangent equation of the curve y = f (x) at point (1,0). (2) find the monotone interval of the function

The function f (x) = x2-x + alnx is known to have the extremum at x = 32. (1) find the tangent equation of the curve y = f (x) at point (1,0). (2) find the monotone interval of the function

(1) F ′ (x) = 2x − 1 + AX = 2x2 − x + ax, ∵ f (x) gets the extremum at x = 32, ∵ f ′ (32) = 0, ∵ 2 × (32) 2 − 32 + a = 0, ∵ a = - 3, which is consistent with the meaning of the problem through the test, ∵ f ′ (x) = 2x2 − x − 3x, ∵ the slope of tangent k = f ′ (1) = - 2, then the tangent of curve y = f (x) at point (1, 0)