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Chapter 2: Q44E (page 77)

The graph of \(f\) is given. State, with reasons, the numbers at which \(f\) is not differentiable.

Short Answer

Expert verified

The number at which \(f\) is not differentiable is \(x = 1\).

Step by step solution

01

Differentiability of the Function

For any given function, the differentiability is defined when its derivatives is having any real value for all particular points that lie within the fixed domain of that function.

02

Find the numbers at which the function is not differentiable.

The given graph is:

Clearly, at \(x = 1\), the function is showing discontinuousnature.

Hence, the number at which \(f\) is not differentiable \(x = 1\).

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Most popular questions from this chapter

35:

  1. For the limit \(\mathop {\lim }\limits_{x \to 1} \left( {{x^3} + x + 1} \right) = 3\), use a graph to find a value of \(\delta \) that corresponds to \(\varepsilon = 0.4\).
  1. By solving the cubic equation \({x^3} + x + 1 = 3 + \varepsilon \), find the largest possible value of \(\delta \) that works for any given \(\varepsilon > 0\).
  1. Put \(\varepsilon = 0.4\) in your answer to part (b) and compare with your answer to part (a).

The table shows the position of a motorcyclist after accelerating from rest.

t(seconds)

0

1

2

3

4

5

6

s(feet)

0

4.9

20.6

46.5

79.2

124.8

176.7

(a) Find the average velocity for each time period:

(i) \(\left( {{\bf{2}},{\bf{4}}} \right)\) (ii) \(\left( {{\bf{3}},{\bf{4}}} \right)\) (iii) \(\left( {{\bf{4}},{\bf{5}}} \right)\) (iv) \(\left( {{\bf{4}},{\bf{6}}} \right)\)

(b) Use the graph of s as a function of t to estimate the instantaneous velocity when \(t = {\bf{3}}\).

Find \(f'\left( a \right)\).

\(f\left( t \right) = {t^3} - 3t\)

(a). Prove Theorem 4, part 3.

(b). Prove Theorem 4, part 5.

If an equation of the tangent line to the curve \(y = f\left( x \right)\) at the point where \(a = {\bf{2}}\) is \(y = {\bf{4}}x - {\bf{5}}\), find \(f\left( {\bf{2}} \right)\) and \(f'\left( {\bf{2}} \right)\).
See all solutions

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