bahozkaleez Posted January 1, 2017 Share Posted January 1, 2017 I am currently reading a book on calculus and I have come across a problem which I can't solve. I do feel like the answer is something simple. Please note that I am fairly new to calculus. Thank you. Link to comment Share on other sites More sharing options...
studiot Posted January 1, 2017 Share Posted January 1, 2017 (edited) What is your definition of f'(x) ? Are you sure the question does not say If f(x) is differentiable at xo then prove that.....etc ? Consider the differentiability of f(x) = |x| and of f(x) =x2 at xo = 0 Edited January 1, 2017 by studiot Link to comment Share on other sites More sharing options...
Function Posted January 1, 2017 Share Posted January 1, 2017 What is your definition of f'(x) ? Are you sure the question does not say If f(x) is differentiable at xo then prove that.....etc ? Consider f(x) = |x| at xo = 0 I've lost all my maths skills (except for statistics), but we always denoted the derivative function of f(x) as f'(x). Link to comment Share on other sites More sharing options...
studiot Posted January 1, 2017 Share Posted January 1, 2017 I've lost all my maths skills (except for statistics), but we always denoted the derivative function of f(x) as f'(x). Yes, that's right the derived function is f'(x). Link to comment Share on other sites More sharing options...
mathematic Posted January 2, 2017 Share Posted January 2, 2017 Place [latex] -f(x_0)+f(x_0)[/latex] in the middle of the numerator. It is obvious what follows. Link to comment Share on other sites More sharing options...
Sriman Dutta Posted January 2, 2017 Share Posted January 2, 2017 By defining f(x)=x^2+3x or anything else, you can put its value in the equation and get the desired results. Link to comment Share on other sites More sharing options...
zztop Posted January 2, 2017 Share Posted January 2, 2017 (edited) I am currently reading a book on calculus and I have come across a problem which I can't solve. I do feel like the answer is something simple. Please note that I am fairly new to calculus. mathz.PNG Thank you. [latex]\frac{f(x_0+\Delta x)-f(x_0-\Delta x)}{2 \Delta x}=\frac{f(x_0+\Delta x)-f(x_0)+f(x_0)-f(x_0-\Delta x)}{2 \Delta x}[/latex] "mathematic" beat me to it Edited January 2, 2017 by zztop 1 Link to comment Share on other sites More sharing options...
Sriman Dutta Posted January 2, 2017 Share Posted January 2, 2017 Hey zztop, you forget the limit. ;-) Link to comment Share on other sites More sharing options...
bahozkaleez Posted January 3, 2017 Author Share Posted January 3, 2017 (edited) [latex]\frac{f(x_0+\Delta x)-f(x_0-\Delta x)}{2 \Delta x}=\frac{f(x_0+\Delta x)-f(x_0)+f(x_0)-f(x_0-\Delta x)}{2 \Delta x}[/latex] "mathematic" beat me to it Thank you, this really helped me. Edited January 3, 2017 by bahozkaleez Link to comment Share on other sites More sharing options...
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