![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Let f (x) = (EX-1) (x-1) K (k = 1,2), then () A. When k = 1, f (x) gets a minimum B at x = 1. When k = 1, f (x) gets a maximum C at x = 1. When k = 2, f (x) gets a minimum d at x = 1. When k = 2, f (x) gets a maximum at x = 1
When k = 1, the function f (x) = (EX-1) (x-1). The derivative function can obtain f '(x) = ex (x-1) + (EX-1) = (xex-1), f' (1) = E-1 ≠ 0, f '(2) = 2e2-1 ≠ 0, then f (x) can not take the extreme value at x = 1 and x = 2. When k = 2, the function f (x) = (EX-1) (x-1) 2. The derivative function can obtain f' (x) = ex (x-1) 2 + 2 (EX-1) (x-1) = (x-1) (xex + EX-2) When x = 1, f '(x) = 0, and when x ＞ 1, f' (x) ＞ 0, when x0 ＜ x ＜ 1 (x0 is the maximum point), f '(x) ＜ 0, so the function f (x) is an increasing function on (1, + ∞), and a decreasing function on (x0, 1), so the function f (x) gets a minimum on x = 1
The image of the function f (x) = x ^ 3-ax ^ 2 + BX = C is a curve e, and there is a point P on the curve, so that the tangent of e at point P is parallel to the X axis, and the relationship between a and B is obtained
When the derivative f '(x) = 3x ^ 2-2ax + B is obtained, and the slope of derivative function is known to be 0, how to calculate Δ?
Δ = 4A ^ 2-4 * 3 * b = 0 (because there is a unique point P)
Given the function f (x) = x & # 179; + ax & # 178; + B, the tangent of the curve y = f (x) at the point (1,1) is y = X. (1) find the monotone interval of a, B (2) find the monotone interval of F (x), and explain its monotonicity in each interval
(1) If f (x) = ax & # 179; - 3x & # 178; / 2 + B is derived, then f '(x) = 3ax & # 178; - 3x has the tangent equation y = 6x-8 at point (2, f (2)), that is, the slope is k = 6, that is, the derivative function f' (2) = 6, that is, f '(2) = 3A × 2 & # 178; - 3 × 2 = 6, and the solution is a = 1, then f (x) = x & # 179; - 3x &
Given the function FX = ax + 1 / x + B, the tangent of the curve y = FX at point (2,1) is parallel to the x-axis 1. Find the analytic formula of F '(x) 2 for FX
A = quarter B = 0
RELATED INFORMATIONS
- 1. Let m and t be real numbers, f (x) = (MX + T) / (x ^ 2 + 1), and the tangent slope of the image of F (x) at point m (0, f (0)) is 1 1. Find the value of real number M 2. If for any x ∈ [1,2], there is always t such that the inequality f (x) ≤ 2T holds, the value range of real number T is obtained 3. Let the two real number roots of the equation x & # 178; + 2tx-1 = 0 be A.B (a < b). If for any x ∈ [a, b], there always exists x1, X2 ∈ [a, b] such that f (x1) ≤ f (x) ≤ f (x2) is constant. Let g (T) = f (x2) - f (x1). When G (T) = 5, find the value of real number t
- 2. When x ∈ (0,1], the function f (x) = x & # 8308; - 2aX & # 178; the slope of the tangent at any point of the image is less than 1, then the value range of the real number a How to be strict after obtaining 4x & # 179; - 4ax < 1?
- 3. Given that the function f (x) = 2lnx-x + a x belongs to [1, e] (where e is the base of natural logarithm), find the function f (x) The known function f (x) = 2lnx-x + a x belongs to the monotone interval of [1, e] (where e is the base of natural logarithm), and the maximum value of known function f (x) is the minimum value of 2ln2
- 4. If the functions f (x) and G (x) are odd and even functions on R respectively and satisfy f (x) + G (x) = ex, where e is the base of natural logarithm, then () A. f（e）＜f（3）＜g（-3）B. g（-3）＜f（3）＜f（e）C. f（3）＜f（e）＜g（-3）D. g（-3）＜f（e）＜f（3）
- 5. Given that the function f (x) = x + ax is an increasing function in the interval [2, + ∞), then the value range of real number a is______ ．
- 6. If inequality (k ^ 2-1) x ^ 2 - (k-1) X-1
- 7. The solution of X inequality: ax + X / 1 > 1, is 1 / X
- 8. For positive numbers x, y, if x + 2Y + xy = 30, then the value range of XY is
- 9. If lgx + lgY = 1, then 5 / x + 2 / y is the minimum
- 10. The function f (x) = x + lgx is known It is proved that f (x) = 3 has real number solution on interval (1,10) If X. Is a real solution of the equation f (x) = 3. € (k, K + 1) finding integer k value
- 11. The function f (x) = ln (1 + x), when x > 0, the inequality f (x) > KX / K + X (K ≥ 0) holds, and the value range of real number k is obtained
- 12. Given that the function f (x) = x / (x * 2 + 1) is an odd function defined on (negative infinity, positive infinity), find the monotone decreasing interval, and judge whether f (x) has a maximum or minimum? If so, write the maximum or minimum
- 13. If the odd function f (x) is a decreasing function in the interval [- B, - A], and the minimum value of F (x) in this interval is 2, then the function f (x) = - | f (x) | in the interval [a, b] is... How monotone, the maximum and minimum case?
- 14. For any real number k, the image of the function y = K (x2-1) + x-a has a common point with the x-axis
- 15. When x ∈ (1, + ∞), the image of function y = XA is always below y = x, then the value range of a is () A. 0 ＜ a ＜ 1b. A ＜ 0C. A ＜ 1 and a ≠ 0d. A ＞ 1
- 16. If the function y = 2Sin (8x + λ) + 2 λ belongs to the symmetry of (0, π) image with respect to x = π / 6, then the number of zeros of the function on the closed interval 0.2 π I want to know what that axis of symmetry tells us. Does the value of λ have anything to do with that?
- 17. It is known that function f (x) satisfies f (a) + F (b) = f (a + b) + 2 for any real number a and B, and if a > 0, f (a) > 2 holds. 1. Find the value of F (0): 2. Prove the increasing function of function f (x) on R
- 18. How to find the minimum positive period of function y = 4sin (2x + π / 3) + 1? Please write it down
- 19. If the function y = 2cos (2x + φ) is odd and is an increasing function on (0, π / 4), then the real number φ may be () A. - π / 2 b.0 C. π / 2 d. π
- 20. A is an internal angle of a triangle, the square of function y = x times cosa-4sina + 6, for any x belongs to R, y is greater than 0!