Given the function f (x) = x2 alnx, G (x) = e ^ X - [x] (1) Proof: e ^ a > A (2) When a > 2E, discuss the number of zeros of function f (x) in the interval (1, e ^ a)

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• 1. Function f (x) = x ^ 2 + 2 / x + alnx If the function is decreasing on [1, positive infinity], find the value range of A If the function increases on [1, positive infinity], find the value range of A
• 2. 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
• 3. The function x ^ 2-alnx (a belongs to R) is known. When x = 1, f (x) has the extremum (1) Finding the value of a (2) Find the number of intersections of F (x) and G (x) = - x ^ 2 + 2x + K (k belongs to R)
• 4. Given function f (x) = LNX - (B / x) (B is a real number) Find the extremum of function f (x) if B = - 1
• 5. Let f (x) be a decreasing function on a set of real numbers. If a + B ≤ 0, then the following is true () A. f（a）+f（b）≤-[f（a）+f（b）]B. f（a）+f（b）≤f（-a）+f（-b）C. f（a）+f（b）≥f（-a）+f（-b）D. f（a）+f（b）≥-[f（a）+f（b）]
• 6. Let f (x) be a decreasing function on a set of real numbers. If a + B ≤ 0, then the following is true () A. f（a）+f（b）≤-[f（a）+f（b）]B. f（a）+f（b）≤f（-a）+f（-b）C. f（a）+f（b）≥f（-a）+f（-b）D. f（a）+f（b）≥-[f（a）+f（b）]
• 7. Parity of F (x) = loga (x + radical x ^ 2 + 1)
• 8. Urgent Teaching: given the square of y = x + 6x + 11, translate its image vector (→ a), get the image of function y = x square, find the vector (→ a) There should be a detailed process
• 9. After translating the image of function y = x ^ 2 according to vector a, the image of function y = x ^ 2 + 6x + 11 is obtained, then vector a is
• 10. The image of the function f (x) = (2-x) / (x-1) is obtained by translating the image of the function f (x) = (1 + x) / X along the position vector a = (m, n), and finding m, n
• 11. Given the function f (x) = x2 + AlN & nbsp; X. (I) when a = - 2, find the extremum of function f (x); (II) if G (x) = f (x) + 2x is a monotone increasing function on [1, + ∞), find the value range of real number a
• 12. The known function f (x) = alnx + 1 / X (1) When a > 0, find the monotone interval and extremum of F (x) (2) When a > 0, for any x > 0, there is ax (2-lnx)
• 13. The known function f (x) = alnx-1 / 2x ^ 2 + 1 / 2 The known function f (x) = alnx-1 / 2x ^ 2 + 1 / 2 (a belongs to R and a is not equal to zero) 1. Find the monotone interval of F (x) 2. Is there a real number a such that for any x belonging to [1, + infinity], f (x) is less than or equal to zero? If so, the value range of a is obtained
• 14. The known function f (x) = {- x ^ 3 + x ^ 2, x = 1 Known function f (x) = {- x ^ 3 + x ^ 2, x = 1 For any given positive real number a, whether there are two points P and Q on the curve y = f (x), such that △ poq is a right triangle with o as the right vertex, and the middle point of the hypotenuse of the triangle is on the y-axis
• 15. Given the function f (x) = x2 + AlN & nbsp; X. (I) when a = - 2, find the extremum of function f (x); (II) if G (x) = f (x) + 2x is a monotone increasing function on [1, + ∞), find the value range of real number a
• 16. Given that the function f (x) = x * x-2x + 3 has a maximum value of 3 and a minimum value of 2 on the closed interval 0 and m, what is the value of M?
• 17. If the function y = x2-2x + 3 has a maximum value of 3 and a minimum value of 2 in the interval [0, M], then the value range of M is () A. [1，∞）B. [0，2]C. （-∞，2]D. [1，2]
• 18. Let f (x) = x2 + X, x < 0-x2, X ≥ 0, if f (f (a)) ≤ 2, then the value range of real number a is___ ．
• 19. If the function f (x) = x & # 178; + 2 (A-1) x + 2 is an increasing function on [4, + ∞), then the value range of real number a is?
• 20. If the function f (x) = {(2b-1) x + B-1, x > 0, is an increasing function on R, then the value range of function B is {- X & # 178; + (2-B) x, X ≤ 0 According to the meaning of the title {2b-1 ＞ 2, ﹛2-b＞0 ﹛b-1≥f（0）, How do these three inequalities come from?