Given the function f (x) = - x ^ 2 + ax + 1-lnx, does the function have both maxima and minima? If so, find out the value range of A. if not, explain the reason

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• 1. Given the function f (x) = x, G (x) = 3 / 8x ^ 2 + LNX + 2. (1) find the maximum and minimum points of the function f (x) = g (x) - 2F (x)
• 2. Given the function f (x) = (KX + 1) / (x2 + C), find the maximum m and minimum m of the function, and the value range of M-M > = 1 Given the function f (x) = (KX + 1) / (x2 + C) (c > 0 and C is not equal to 1, K belongs to R), find the maximum m and minimum m of the function, and the value range of K when M-M > = 1 K radical 2 Thank you first
• 3. It is known that the function f (x) = KX + bx2 + C (C ＞ 0 and C ≠ 1, K ＞ 0) has a maximum point and a minimum point, and one of the extreme points is x = - C (1). Find another extreme point of function f (x). (2) let the maximum of function f (x) be m and the minimum be m. if M-M ≥ 1 is constant for B ∈ [1, 32], find the value range of K
• 4. Given the function f (x) = (KX + 1) / (x2 + C) (c > 0 and C is not equal to 1, K belongs to R), find the maximum value m and minimum value m of the function, and the value of K when M-M > = 1 Given the function f (x) = (KX + 1) / (x2 + C) (c > 0 and C is not equal to 1, K belongs to R), find the maximum m and minimum m of the function, and the value range of K when M-M > = 1
• 5. Given the function f (x) = TaNx, X belongs to 0 to 90 degrees, if X1 and X2 belong to 0 to 90 degrees, and x1 ≠ X2, the proof is: 1 / 2 {f (x1) + F (x2)} > F {(x1 + x2) / 2}
• 6. Given the function f (x) = TaNx, X belongs to (0 ~ π / 2) and X1 = X2, compare the size of 1 / 2 (FX1 + FX2) and f (x1 + x2) / 2 Can we not use derivatives
• 7. Given the function f (x) = TaNx, X belongs to (0, Wu / 2), if x1, X2 belong to (0, Wu / 2), X1 is not equal to X2, try to prove: 1 / 2 [f (x1) + F (x2)] > F [(x1 Given the function f (x) = TaNx, X belongs to (0, Wu / 2), if x1, X2 belong to (0, Wu / 2), X1 is not equal to X2, try to prove: 1 / 2 [f (x1) + F (x2)] > F [(X1 + x2) / 2]
• 8. Even functions defined on R satisfy the following conditions: for any X &;, X &; ∈ [0, + ∞], there is f (x1) - f (x2) / x1-x2 ＜ 0 The size order of F (3), f (- 2), f (1) (solving process)
• 9. The even function f (x) defined on R satisfies that for any x1, X2 belongs to (negative infinity, 0) (x1 ≠ x2), and (x2-x1) (f (x2) - f (x1)) > 0, then when n belongs to N +, f（n+1）
• 10. The zero point of the function f (x) = x2-3x + 2 is () A. （1，0），（2，0）B. （0，1），（0，2）C. 1，2D. -1，-2
• 11. If the function f (x) = x ^ 3 + 2x ^ 2-ax + 3 has both minimum and maximum, then the value range of a is?
• 12. Let the square of function f (x) = x (x-a) have a maximum at x = 2, and find the value of real number a
• 13. If the function f (x) = x · (x-C) 2 has a maximum at x = 2, then the value of constant C is () A. 6B. 2C. 2 or 6D. 23
• 14. Given the function f (x) = MX / (square of X + n), m and N belong to R, and the maximum value 2 is obtained at x = 1 1. Find the analytic expression of function f (x) 2. Find the maximum of function f (x)
• 15. Let the function f (x) = - 1,3x3 + x2 + (M2-1) x belong to R, and find the monotone interval and extremum of the function
• 16. F (x) = 1 / 3x3 + 1 / 2ax2 + AX-2. A ∈ R. if the function f (x) is a monotone increasing function on (- ∞, + ∞), find the value range of A
• 17. Given that the function f (x) = 1 / 3 x & # 179; + 1 / 2 ax & # 178; + BX has an extreme point in the interval [- 1,1), (1,3], then the value range of a-4b is
• 18. The function f (x) = 1 / 3x3-1 / 2ax2 + 2 / 3a, where a > O, if x > = 0, f (x) > 0 holds, the value range of a is obtained
• 19. Find the expression of M (a) when the minimum value of function f (x) = x ^ 2 + 2aX + 3 is m (a)
• 20. Let f (x) = x ^ 2-2ax + 1 (a is a real number) be g (a) when - 2 ≤ x ≤ 1 Find g (a) expression, monotone interval, range