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

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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

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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