Determine if the following piecewise-defined function is differentiable at the origin.4х -– 6x3- 1,X20f(x) =13x -X +1x< 0.....The functiondifferentiable at the origin because the limits limf(0 + h) – f(0)f(0 + h) – f(0)and limareh→0h→0(Type integers or simplified fractions.)

Determine if the following piecewise-defined function is differentiable at the origin. 4x - 6x° - 1, x20 f(x) = { 1 3x - X+1 x<0 ..... f(0 + h)-f(0), f(0 + h)-f(0) The function differentiable at the origin because the limits lim and lim are h→0 h→0 (Type integers or simplified fractions.)

Determine if the following piecewise-defined function is differentiable at the origin. 4x - 6x° - 1, x20 f(x) = { 1 3x - X+1 x<0 ..... f(0 + h)-f(0), f(0 + h)-f(0) The function differentiable at the origin because the limits lim and lim are h→0 h→0 (Type integers or simplified fractions.)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Determine if the following piecewise-defined function is differentiable at the origin.
4х -
– 6x3
- 1,
X20
f(x) =
1
3x -
X +1
x< 0
.....
The function
differentiable at the origin because the limits lim
f(0 + h) – f(0)
f(0 + h) – f(0)
and lim
are
h→0
h→0
(Type integers or simplified fractions.)

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