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The slope of the function f(x)= (3x-5)^7 has an integer value at x= 2. Use some sort of numerical method to determine what it is.

 Jul 1, 2015

Best Answer 

 #1
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f(x)  = (3x -5)^7    ....the derivative of this function will give us the slope at any  x value.....so...

 

f ' (x)  =   [7(3x - 5)^6 ]* (3)  =  21(3x -5)^6     ....... so.......

 

f ' (2)  = 21(3(2) - 5)^6  =   21(6 -5)^6  =  21(1)^6   = 21

 

And when x = 2, y = 1.......her's a graph of the tangent line to the function at that point...https://www.desmos.com/calculator/x9cy77qjdk

 

  

 Jul 1, 2015
 #1
avatar+128079 
+5
Best Answer

f(x)  = (3x -5)^7    ....the derivative of this function will give us the slope at any  x value.....so...

 

f ' (x)  =   [7(3x - 5)^6 ]* (3)  =  21(3x -5)^6     ....... so.......

 

f ' (2)  = 21(3(2) - 5)^6  =   21(6 -5)^6  =  21(1)^6   = 21

 

And when x = 2, y = 1.......her's a graph of the tangent line to the function at that point...https://www.desmos.com/calculator/x9cy77qjdk

 

  

CPhill Jul 1, 2015

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