Finding the extremum of a given function f (x) = x-alnx (a ∈ R)

RELATED INFORMATIONS

• 1. Given the function f (x) = alnx + 2 / x + X, 1, where a belongs to R. if a = 1, find the extreme point of F (x) 2. If f (x) increases in the interval [1, + infinity], find the value range of A
• 2. Let f (x) = X-2 / x-alnx. When a = 3, find the extremum of FX
• 3. For the cubic function f (x) = x ^ 3-3x ^ 2-3mx + 4 (M is a constant), the monotone interval of F (x) is obtained
• 4. Given the square of the algebraic formula x + ax + B, when x = - 1, its value is 5; when X-1, its value is - 1. Find the value of a and B
• 5. In the square + BC of the algebraic expression ax, if x = 5, its value is 45 and x = - 2, its value is 10, then a = B=
• 6. Given the square of the algebraic formula ax + BX + 2, when x = 1, its value is 1:; when x = - 1, its value is 5. Find the value of a and B
• 7. If x = 1, the value of the algebraic formula ax * ax * ax + BX + 7 is 4. Then when x = - 1, what is the value of the algebraic formula ax * ax * ax + BX + 7?
• 8. -6 3 5 - 4 - 2 7 find the next number
• 9. A good place to read --- the way to the supermarket --- go straight along Daqiao street-------- English Chinese Translation Tour guide-------- A good place to read---------- The way to the supermarket------------- Go straight along Daqiao street------------
• 10. On the map of 1:250000 scale, the distance between the two cities is 12 cm. On the map of 1:1000000 scale, what is the distance between the two cities? A chemical fertilizer plant produces a batch of chemical fertilizers, 90 tons in the first five days. According to this calculation, it took 12 days to produce this batch of chemical fertilizers. How many tons are there in this batch of chemical fertilizers With the above question: () and () are in proportion, () must be
• 11. How to judge whether the extreme point is a maximum or a minimum in the derivative function Such as the title
• 12. Find the extremum of binary function f (x, y) = x ^ 2 + y ^ 3 + 4x-3y + 4, and explain whether it is a maximum or a minimum
• 13. FX = ax ^ 2 + LNX if FX1 = (A-1 / 2) x ^ 2 + 2aX + (1-A ^ 2) LNX, FX2 = 1 / 2x ^ 2 + 2aX On (1, positive infinity), FX has FX1 in the common domain
• 14. We know the function FX = x Λ 2 + 2x + 4, if X1 + x2 = 0 and X1 = 0
• 15. Given the quadratic function y = AX2 + BX + C, when the independent variable x takes X1 and X2, the function values are equal, then how to write the function when the independent variable x takes X1 + x2?
• 16. Let f (x) = ax ^ 2 + BX (a ≠ 0) satisfy the condition 1. F (- 1 + x) = f (- 1-x); there is only one common point between the image of 2 function f (x) and the line y = X
• 17. It is known that the quadratic function f (x) = ax ^ 2 + BX holds f (x minus 4) = f (2 minus x) for any x belonging to R, and the image of the function passes through a (1,3 / 2) (1) to find the function Given that the quadratic function f (x) = ax ^ 2 + BX belongs to R for any x, f (x minus 4) = f (2 minus x) holds, and the image of the function passes through a (1,3 / 2) (1) find the analytic expression of the function y = f (x) (2) if the solution set of the inequality f (x minus t) is less than or equal to x [4, M], find the value of the real number T, M
• 18. Given that the image of the function f (x) = AX3 + bx2 passes through the point m (1,4), the tangent of the curve at the point m is just perpendicular to the straight line x + 9y = 0. (1) find the value of real numbers a and B; (2) if the function f (x) monotonically increases in the interval [M, M + 1], find the value range of M
• 19. Let f (x) = AX2 + BX + C (a ≠ 0), y = f (x) pass through the point (0, 2A + 3), and the tangent at the point (- 1, f (- 1)) is perpendicular to the Y axis. (1) use a to represent B and C respectively; (2) when B · C reaches the minimum, find the monotone interval of the function g (x) = - f (x) · ex
• 20. Given the function f (x) = X3 + AX2 + BX + C, the tangent l of the curve y = f (x) at the point x = 1 is only the fourth quadrant, and the slope is 3, and the distance from the origin of the coordinate to the tangent L is 1010, if x = 23, y = f (x) has extremum. (1) find the value of a, B, C; (2) find the maximum and minimum value of y = f (x) on [- 3, 1]