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Home > Calculus calculators > Derivative > Increasing and decreasing functions at point example
10. Increasing and decreasing functions at point example ( Enter your problem )
( Enter your problem )
  1. Method & Example `f(x)=x^3-3x^2+7`, at point x = 1,3
  2. Example `f(x)=x^2-4x`, at point x = -1,0,3
  3. Example `f(x)=x^3-3x+2`, at point x = 0,2
  4. Example `f(x)=-2x`, at point x = 1
 		Other related methods
  1. First Derivative
  2. Second Derivative
  3. Third Derivative
  4. Fourth Derivative
  5. nth Derivative / Higher order Derivative
  6. Derivative at a Point
  7. First derivative test for Local maxima and minima
  8. Second derivative test for Local maxima and minima
  9. Critical Points and Extrema
  10. Increasing and decreasing functions at point
  11. Increasing and decreasing intervals
1. Method & Example `f(x)=x^3-3x^2+7`, at point x = 1,3
(Previous example)		3. Example `f(x)=x^3-3x+2`, at point x = 0,2
(Next example)

2. Example `f(x)=x^2-4x`, at point x = -1,0,3


`f(x)=x^2-4x`
Find Increasing and decreasing functions at point x = -1,0,3

Solution:
Here, `f(x)=x^2-4x`

Step-1: Find the derivative of the function
`:. f^'(x)=``d/(dx)(x^2-4x)`

`=d/(dx)(x^2)-d/(dx)(4x)`

`=2x-4`


Step-2: Determine if the function is increasing or decreasing at given points
1. At `x=-1`

`f^'(-1)``=2*(-1)-4`

`=-2-4`

`=-6`` < 0`

`:.` Function is decreasing at `x=-1`

2. At `x=0`

`f^'(0)``=2*0-4`

`=0-4`

`=-4`` < 0`

`:.` Function is decreasing at `x=0`

3. At `x=3`

`f^'(3)``=2*3-4`

`=6-4`

`=2`` > 0`

`:.` Function is increasing at `x=3`




This material is intended as a summary. Use your textbook for detail explanation.
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1. Method & Example `f(x)=x^3-3x^2+7`, at point x = 1,3
(Previous example)		3. Example `f(x)=x^3-3x+2`, at point x = 0,2
(Next example)


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