Purchase Solution

definition of derivative

Not what you're looking for?

Ask Custom Question

Let
f(x)={(x^3)cos(1/x) if xâ? 0, 0 if x=0,
and
g(x)={(1/x)sin(x) if xâ? 0, 0 if x=0.

a) Using the definition of the derivative show that f is differentiable at 0 and determine f '(0).
b) Is g differentiable at 0? Justify your answer.
c) Show that f ' ^(x) and g ' ^(x) exist for xâ? 0 and determine their values.

Attachments
Purchase this Solution
Solution Summary

This solution shows how to use the definition of derivative to show that given variables are or are not differentiable at 0.

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

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.

Multiplying Complex Numbers

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

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Definition of the Derivative & Questions

    The derivative of the derivative of is denoted by: or sometimes by . 1. Use the definition of derivative to calculate where . 2. Use the definition of derivative to calculate where . 3.

  • Basic Differenitation Formulas

    Solution: By using definition of derivative By using algebra of limits Lim(cf(x)) = cLim (f(x)) By using definition of derivatives Hence, g'(x) = cf'(x) (d) Use the definition of the derivative to write out the derivative of

  • Limit definition of derivative

    4219 Find the derivative of a quadratic polynomial. Use the (limit) definition of the derivative to find the derivative of f(x)=3x^2-2x+1?

  • Definition of derivative

    4032 Definition of derivative Let f(x) be a continuous function of one variable. a) Give the definition of the derivative.

  • Derivative

    17742 Use the Definition of a Derivative See attached 1) Use the definition of a derivative to find G (x) if G(x) = See the attached file. 1) Use the definition of a derivative to find G (x) if G(x) = G(x) = 2/(x-1)....taking

  • Limit Definition of the Derivative

    135915 Limit Definition of the Derivative Let g(x) = x^2 + x.

  • Definition of the Derivative

    405202 Definition of the Derivative The derivative of a continuous function at x is the slope of the tangent line to the curve at x.

  • Definition of the Derivative and Limits : Finding the Slope of a Tangent Line

    43643 Definition of the Derivative and Limits: Slope of Tangent Line Use the definition of the derivative to find the slope of the tangent line to the graph of f(x) = 1/(3x -2) at x = 1. See the attached file.

  • derivative of the function

    Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value x = c. (Compute the derivative of the function from the definition only, using limits.

  • Definition of Derivatives

    4355 Show me how to use the definition of the derivative. The process of working with the definition of the derivative is shown using the example f(x)=3x-6.

View More Related Solutions