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Consider the piecewise-defined function f defined by8 -3x211 6x{if x 1if x 1f(x)Find f'(1). Iff is not differentiable at the number c =1, enter DNEf'(1)

Question
Consider the piecewise-defined function f defined by
8 -3x2
11 6x
{
if x 1
if x 1
f(x)
Find f'(1). Iff is not differentiable at the number c =
1, enter DNE
f'(1)
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Consider the piecewise-defined function f defined by 8 -3x2 11 6x { if x 1 if x 1 f(x) Find f'(1). Iff is not differentiable at the number c = 1, enter DNE f'(1)

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check_circleAnswer
Step 1

Given,

8-3.x2 if x >1
f (x)=11-6x if xsl
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8-3.x2 if x >1 f (x)=11-6x if xsl

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Step 2

A function f is said to be differentiable at a point c, if

f(c+h) (c) and lim
lim
f(c+h)-f(c)
are finite and equal
h
h
h0
0
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f(c+h) (c) and lim lim f(c+h)-f(c) are finite and equal h h h0 0

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Step 3

Therefore,

&nb...

f(1+h)-(1)11-6(1+h)-5
lim
h
h
h+0
0
-6h
- lim
h
h0
-lim(-6)
0
= -6
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f(1+h)-(1)11-6(1+h)-5 lim h h h+0 0 -6h - lim h h0 -lim(-6) 0 = -6

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Tagged in

Math

Calculus

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