![](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>)
What is the relationship between derivative function and monotonicity of function? What is the relationship between derivative function and monotonicity of function? How to draw function image by derivative function, or draw derivative function by function? Please give specific examples. Is there a better way to remember them?
If the derivative function is greater than 0, then the function monotonically increases, less than 0, decreases, and equals 0, then the image is a straight line parallel to the X axis. The image of the derivative function corresponds to the tangent point of the corresponding function
You usually do this type of topic, pay attention to its meaning, naturally understand, practice makes perfect
RELATED INFORMATIONS
- 1. How to find the symmetry axis, monotonicity and parity of trigonometric functions?
- 2. Let y = f (x) be an odd function on the domain R, and f (X-2) = - f (x) holds for all x belonging to R, then the symmetry axis of F (x) image?
- 3. If the function defined on R, y = f (x), and the image of y = f (x + 2) is symmetric with respect to x = 0, then the symmetry axis of the image of the function y = f (x)
- 4. Given the function f (x) = log, take a as the base 1 + X / 1-x (a > 0, a ≠ 1) to find the inverse function
- 5. The inverse function of function f (x) log with base 2 (x + 1) (x > = 0) is f ^ - 1 (x)=
- 6. If the inverse function of function f (x) is f ^ (- 1) (x) = log with 2 as the base x, then f (x)=
- 7. The inverse function f ^ - 1 (x) = () of function f (x) = log (2) (1 + 1 / x) (x > 0)
- 8. The monotone increasing interval of function f (x) = log5 (2x + 1) is______ ．
- 9. The monotone increasing interval of function f (x) = log5 (2x + 1) is______ ．
- 10. Given that the function f (x) = log (2∧x-1) (a > 0, and a ≠ 1) always has f (x) > 0 in the interval (0,1), then the monotone increasing interval of the function y = log ∨ a (X & # 178; - 2x-3) is
- 11. Draw the graph of function f (x) = | x ^ 2 + X-2 | and write the monotone interval
- 12. Let the function FX = x + A / x + B (a > b > 0), find the monotone interval of F (x), and prove the increasing of F (x) in its monotone interval Sex
- 13. F (x) = x2 + 4x + 3, t ∈ R, the function g (T) represents the minimum value of function f (x) in the interval [T, t + 1], and the expression of G (T) is obtained
- 14. The minimum value of the function f (x) = x2-4x-4 in the closed interval [T, t + 1] (t ∈ R) is denoted as G (T). (1) try to write the functional expression of G (T). (2) make the image of G (T) and find the minimum value of G (T)
- 15. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 16. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 17. FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX
- 18. Let f (x) = x ^ 2-2x + 2, let the minimum value of F (x) on [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 19. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 20. Let the minimum value of F (x) = x2-4x-4 on [T, t + 1] (t belongs to R) be g (T). Write out the functional expression of G (T)