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How to determine whether x, y is a maximum or a minimum?
If it's a practical problem, it's the point you want. If other, you can substitute stationary point and endpoint for comparison
Extremum of function f (x) = x ^ 2 + alnx (a ∈ R)
The domain is x > 0
f'(x)=2x+a/x=1/x*(2x^2+a)
If a > = 0, then the function increases monotonically in the domain x > 0 and has no extremum
If a
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 y when x = - 2
When x = - 1, its value is 5; when x = 1, its value is - 1; when x = - 2, y = 11
RELATED INFORMATIONS
- 1. When x = 2, the cube + BX-1 of the algebraic formula ax equals 6. When x equals - 2, what is the value of this formula?
- 2. When x = 2, the value of the algebraic expression ax & # 179; + BX + 1 is 6, then when x = - 2, ax & # 179; + BX + 1 =?
- 3. It is known that when x = - 1, the value of the algebraic formula ax & # 179; + BX + 6 is - 10. When x = 1, find the value of the algebraic formula ax & # 179; + BX + 6
- 4. There are several equations 120% X-70% x = 30-25% x = 10
- 5. Is 30 + 25 = x the equation?
- 6. 30 / x + 25 = 85 the process of solving equation
- 7. 2x^2+xy-6x^2+5x-4y+2
- 8. Given x + y = 6, xy = 4, then the value of X2Y + XY2 is______ ．
- 9. Extremum of derivative Others say that "when we ask whether there is a straight point in the big derivative problem, we must take the number on both sides of the plant to test after finding out that the derivative is equal to zero." It seems so, but how to test it?
- 10. On the extremum of derivative The book says, "generally, the steps to find the maximum and minimum values of the function y = f (x) on [a, B} are as follows: 1. Find the extremum of function y = f (x) in (a, b); 2. Compare the extremum of function y = f (x) with the function values f (a) and f (b) at the breakpoint, where the largest one is the maximum and the smallest one is the minimum Question: is the extremum mentioned in 1 f '(x) = 0? Is the derivative value of the extremum point necessarily 0? Is it not the upper minimum and maximum value collectively referred to as extremum? Then the extremum has been found in 1, is it not the maximum and minimum value? Why should we calculate the second step?
- 11. In the sufficient condition of the extremum of binary function, when AC-B ^ 2 > 0, will there be a > 0, C0, which is the minimum value, a or C
- 12. Find the extremum of the function z = x ^ 2-xy + y ^ 2-3y, and point out the maximum and minimum Need calculus process
- 13. f(x)=(ax^2-x)(lnx-1/2ax^2+x)
- 14. It is known that the quadratic function f (x) = ax ^ 2 + BX satisfies the condition 1. For any x belonging to R, f (x-4) = f (2-x) 2. The image of function f (x) is tangent to the line y = X The quadratic function f (x) = ax ^ 2 + BX satisfies the condition 1. For any x belonging to R, f (x-4) = f (2-x) 2. The image of function f (x) is tangent to the line y = X Find: if and only if x belongs to [4, M], f (x-t) ≤ x is constant, try to find the value of T M
- 15. If the quadratic function f (x) = - x ^ 2 + BX + C is a decreasing function in the interval (2, + ∞), and an increasing function in the interval ((∞), 2), its function and X axis intersect at two points a and B, and | ab | = 6, let g (x) be defined as an even function in R, when x > = 0, G (x) = f (x), and write the monotone interval of G (x)
- 16. If the right graph is a partial image of the quadratic function f (x) = x ^ 2-bx + A, then G (x) = ln x + F ′ (x) is zero
- 17. Given that the image of the function f (x) = ax 3 + 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. Find the values of a and B Hurry! Where's the exam（
- 18. Given that the image of the function f (x) = AX2 + BX3 passes through point m (1,4), the tangent of the curve at point m is just perpendicular to the straight line x + 9y = 0 1. Find the value of real numbers a and B 2. Calculate the value range of the slope of the tangent at a certain point on the known function image
- 19. Given that the image of function f (x) = (AX2 + BX + C) E-X passes through a point (0, 2a), and the inclination angle of the tangent at this point is 45 ° (1) B, C are represented by a; (2) if f (x) is a monotone increasing function on [2, + ∞), the value range of a is obtained
- 20. If the even function f (x) is an increasing function in the interval [3,7], and the maximum value is 5, then f (x) is an increasing function in the interval [- 3, - 7]