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In this lesson, we will learn how to determine whether a function is differentiable and identify the relation between a functionβs differentiability and its continuity.

Q1:

Given that is a continuous function, find the value of π . What can be said of the differentiability of π at π₯ = β 2 ?

Q2:

Suppose What can be said of the differentiability of π at π₯ = β 1 ?

Q3:

Discuss the differentiability of the function π at π₯ = 1 given

Q4:

Suppose What can be said of the differentiability of π at π₯ = 4 ?

Q5:

Let Determine the values of π and π so that π is continuous at π₯ = β 2 . What can be said of the differentiability of π at this point?

Q6:

Suppose Find the value of a such that the function π is continuous at π₯ = 0 , and then discuss the differentiability of π at π₯ = 0 .

Q7:

Find the values of π and π and discuss the differentiability of the function π at π₯ = β 1 given π is continuous and

Q8:

What can be said of the differentiability of π ( π₯ ) = β π₯ + 4 π₯ + 4 2 at π₯ = β 2 ?

Q9:

What can be said of the differentiability of π ( π₯ ) = 9 π₯ + 8 π₯ + 7 ο¨ at π₯ = β 2 ?

Q10:

Discuss the differentiability of the function π at π₯ = β 4 given

Q11:

Suppose What can be said of the differentiability of π at π₯ = 1 ?

Q12:

Let Determine the value of π so that π is continuous at π₯ = 2 . What can be said of the differentiability of π at this point?

Q13:

Discuss the differentiability of the function π ( π₯ ) at π₯ = 1 given π ( π₯ ) = ( 6 π₯ β 6 ) | 6 π₯ β 6 | .

Q14:

Find the values of π and π given the function π is differentiable at π₯ = 1 where

Q15:

Find the values of π and π given the function π is differentiable at π₯ = β 1 where

Q16:

Discuss the differentiability of the function π at π₯ = β 8 given

Q17:

Discuss the differentiability of the function π at π₯ = 6 , given

Q18:

Q19:

Suppose What can be said of the differentiability of π at π₯ = β 8 ?

Q20:

Suppose What can be said of the differentiability of π at π₯ = β 6 ?

Q21:

Let If π ( 1 ) = 1 2 and π is continuous at π₯ = 1 , determine the values of π and π . What can be said of the differentiability of π at this point?

Q22:

Discuss the differentiability of a function π at π₯ = β 4 given

Q23:

Discuss the differentiability of the function π ( π₯ ) = β 4 π₯ + 1 π₯ at π₯ = β 7 .

Q24:

Let Determine the values of π and π so that π is continuous at π₯ = 1 . What can be said of the differentiability of π at this point?

Q25:

Discuss the continuity and differentiability of the function π at π₯ = 0 given

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