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.

What is your definition of f'(x) ?

 

Are you sure the question does not say

 

If f(x) is differentiable at x_o then prove that.....etc ?

 

Consider the differentiability of f(x) = |x| and of f(x) =x² at x_o = 0

 

 

 

Edited January 1, 20178 yr by studiot

What is your definition of f'(x) ?

 

Are you sure the question does not say

 

If f(x) is differentiable at x_o then prove that.....etc ?

 

Consider f(x) = |x| at x_o = 0

 

I've lost all my maths skills (except for statistics), but we always denoted the derivative function of f(x) as f'(x).

 

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).

Place [latex] -f(x_0)+f(x_0)[/latex] in the middle of the numerator. It is obvious what follows.

By defining f(x)=x^2+3x or anything else, you can put its value in the equation and get the desired results.

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.

 

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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, 20178 yr by zztop

Hey zztop, you forget the limit.

;-)

[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, 20178 yr by bahozkaleez