Increasing and decreasing functions at point Example f(x)=-2x, at point x = 1

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Home > Calculus calculators > Increasing and decreasing functions at point example

4. Increasing and decreasing functions at point example ( Enter your problem )

( Enter your problem )

Method & Example `f(x)=x^3-3x^2+7`, at point x = 1,3
Example `f(x)=x^2-4x`, at point x = -1,0,3
Example `f(x)=x^3-3x+2`, at point x = 0,2
Example `f(x)=-2x`, at point x = 1

Other related methods

Derivative
Local maxima and minima of a function using second derivative test
Local maxima and minima of a function using first derivative test
Increasing and decreasing functions at point
Increasing and decreasing intervals of a function

3. Example `f(x)=x^3-3x+2`, at point x = 0,2
(Previous example)

5. Increasing and decreasing intervals of a function
(Next method)

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

`f(x)=-2x`
Find Increasing and decreasing functions at point x = 1

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

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

`=-2`

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

`f^'(1)``=-2`` < 0`

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

This material is intended as a summary. Use your textbook for detail explanation.
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