×
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 69ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 69ae

×

# x 5x+6 Is it differentiable Is f(x) = x2 differentiable at

ISBN: 9780321570567 2

## Solution for problem 69AE Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendentals | 1st Edition

4 5 1 299 Reviews
20
5
Problem 69AE

x ?5x+6 Is it differentiable?? Is f(x) = x?2 differentiable at x = 2? Justify your answer.

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 2 (x3)(x2) Given f(x) = x 5x+6= = x 3 x2 x2 STEP 2 We need to find whether f(x)=x-3 is differentiable at x=2. For that ,we consider the left and right hand derivatives of the function at x=2. The left hand derivative of f(x) at x=2 is f(2+h)f(2) f(2) = lim = lim 2+h32+3 = lim h = 1 h2 h h2 h h2 h The right hand derivative of f(x) at x=2 is f(2+h)f(2) 2+h32+3 h f+(2) = lim+ h = lim + h = lim +h = 1 h2 h2 h2 Therefore we have f (2+ = f () Thus the function f(x) is differentiable at x=2. x 5x+6 The graph of f(x) = x2 = x 3 can be drawn as

Step 2 of 3

Step 3 of 3

#### Related chapters

Unlock Textbook Solution