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July 21st, 2016, 07:24 AM  #1 
Newbie Joined: Jul 2016 From: pickering Posts: 7 Thanks: 2  instantaneous rate of changes
Given the function g(x)=x^42x^3+1, a)Estimate the instantaneous rate of change at x=1 , b. Will the instantaneous rate of change be the same at any xvalue on the function? Explain why or why not. i need help thank you 
July 21st, 2016, 07:29 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
First tell us what you understand 'instantaneous rate of change ' to mean.

July 21st, 2016, 07:29 AM  #3 
Senior Member Joined: Apr 2014 From: UK Posts: 937 Thanks: 335 
Are you familiar with differentiation?

July 21st, 2016, 07:38 AM  #4 
Newbie Joined: Jul 2016 From: pickering Posts: 7 Thanks: 2  
July 21st, 2016, 07:41 AM  #5 
Newbie Joined: Jul 2016 From: pickering Posts: 7 Thanks: 2  
July 21st, 2016, 07:54 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575  
July 21st, 2016, 07:57 AM  #7 
Newbie Joined: Jul 2016 From: pickering Posts: 7 Thanks: 2  
July 21st, 2016, 08:04 AM  #8 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
That would do although you should not blindly apply any formula, without knowing what it means. So is f(x) clear enough? What do you think h might be? remember the question said estimate the rate of change, not calculate its exact value. 
July 21st, 2016, 08:13 AM  #9 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
If in doubt, ask.

September 15th, 2016, 11:14 PM  #10 
Newbie Joined: Jun 2016 From: india Posts: 24 Thanks: 4 
Given function : $\displaystyle g(x)=x^42x^3+1$ To find rate of change, we have to differentiate given function. $\displaystyle \dfrac{d}{dx}\;\{g(x)\}=\dfrac{d}{dx}\;(x^42x^3+1)$ $\displaystyle \Rightarrow\;g'(x)=4x^36x^2+0$ To find instantaneous rate of change at $\displaystyle x=1$, put $\displaystyle x=1$ in $\displaystyle g'(x)$. So instantaneous rate of change at $\displaystyle x=1$ $\displaystyle =4(1)^36(1)^2$ $\displaystyle =46$ $\displaystyle =2$ If you want to study more about rate of change and approximation, this will help you. Rate of Change Formula, Rate of Change of Volume and Surface, Velocity  Actucation 

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