Finding the derivative when x equals 0

KF33 · Jun 26, 2016

Homework Statement

I have been working on the problem below and I am stuck. I am stuck primarily because of the part where is says x=0. If x-0, it should cancel everything out. The derivative of 0 is 0 so will cancel everything out I think, so I am not sure if that is the reasoning and the proof behind it.

Homework Equations

The Attempt at a Solution

I thought I should start this way, but I am not 100% sure.[/B]

Handwritten-style math: rewrite the quotient as (1/c) times [ (f(ax) - f(a·0))/x - (f(bx) - f(b·0))/x ].

SammyS · Jun 26, 2016

KF33 said:

Homework Statement

I have been working on the problem below and I am stuck. I am stuck primarily because of the part where is says x=0. If x-0, it should cancel everything out. The derivative of 0 is 0 so will cancel everything out I think, so I am not sure if that is the reasoning and the proof behind it.

Homework Equations

The Attempt at a Solution

I thought I should start this way, but I am not 100% sure.[/B]
View attachment 102534

It's a good idea to have the problem statement visible in the OP.

Typeset statement: Prove that if f : R to R is differentiable at x = 0 and a, b, c in R with c not equal to 0, then the limit as x approaches 0 of (f(ax) - f(bx))/(cx) equals (a - b)/c times f'(0).

James R · Jul 5, 2016

L'Hopital's rule?

micromass · Jul 6, 2016

James R said:

L'Hopital's rule?

Not necessary with the hint in the OP, the definition of a derivative is enough.

Finding the derivative when x equals 0

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

Homework Statement

Homework Equations

The Attempt at a Solution

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