(a) Explanation f ' ( a ) is nothing but the derivative of a function at a number a. The derivative of a function at a number ‘a’ which is denoted by f ' ( a ) can be written as f ' ( a ) = lim h → 0 f ( a + h ) − f ( a (b) To determine The relationship between differentiability and continuity of a function. (c) To determine To sketch: The graph of a function which is continuous and not differentiable at a = 2.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3, Problem 5CC

(a)

To determine

The meaning of function f to be differential at ‘a’.

(b)

To determine

The relationship between differentiability and continuity of a function.

(c)

To determine

To sketch: The graph of a function which is continuous and not differentiable at a = 2.

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Chapter 3, Problem 4CC

Chapter 3, Problem 6CC

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Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) Function x-Value Differential of x Ду = dy = y = x² + 2 x = -4 Ax = dx = 0.01

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Chapter 3 Solutions

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The meaning of function f to be differential at ‘a’.

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The meaning of function f to be differential at ‘a’.

The relationship between differentiability and continuity of a function.

To sketch: The graph of a function which is continuous and not differentiable at a = 2.

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Chapter 3 Solutions