Increasing and decreasing functions at point Method & Example f(x)=x^3-3x^2+7, at point x = 1,3

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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

3. Local maxima and minima of a function using first derivative test
(Previous method)

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

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

`f(x)=x^3-3x^2+7`
Find Increasing and decreasing functions at point x = 1,3

Solution:
Here, `f(x)=x^3-3x^2+7`

Step-1: Find the derivative of the function
`:. f^'(x)=``d/(dx)(x^3-3x^2+7)`

`=d/(dx)(x^3)-d/(dx)(3x^2)+d/(dx)(7)`

`=3x^2-6x+0`

`=3x^2-6x`

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

`f^'(1)``=3*1^2-6*1`

`=3-6`

`=-3`` < 0`

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

2. At `x=3`

`f^'(3)``=3*3^2-6*3`

`=27-18`

`=9`` > 0`

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

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