# Differentiable and continuous functions

Not what you're looking for?

Suppose fâ?¶Râ?'R is twice differentiable with both f' and f'' continuous in an interval around 0. Suppose further that f(0)=0. Let

h(x)={f(x)/x, if xâ? 0,

f^' (0), if x=0.

Show that

(a) h is differentiable at x=0.

(b) h is differentiable at x=0 with h^' (0)=1/2 f^'' (0).

(c) h' is continuous at x=0.

##### Purchase this Solution

##### Solution Summary

Differentiables and continuous functions are clearly exhibited.

##### Solution Preview

Proof:

Since is twice differentiable function, and are continuous in the neighborhood of 0, and , then we have

, where ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.