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Chapter 2: Q49E (page 77)

The figure shows the graphs of \(f\), \(f'\), and \(f''\). Identify each curve, and explain your choices.

Short Answer

Expert verified

\(\begin{array}{l}a &=& f\\b &=& f'\\c &=& f''\end{array}\)

Step by step solution

01

Differentiation of the Function

The differentiation of any function can be defined as a method to find the slope of the function, in which the function needs to be differentiable and continuous in nature.

02

Identifying the curves.

The given graph is:

Clearly, the curve b is appear to be the slope of the curve a, and the curve c is seems to be the slope of curve b.

If the curves are to be represented in form of functions, then:

\(\begin{array}{l}a &=& f\\b &=& f'\\c &=& f''\end{array}\)

Hence, this is the required answer.

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Most popular questions from this chapter

A roast turkey is taken from an oven when its temperature has reached \({\bf{185}}\;^\circ {\bf{F}}\) and is placed on a table in a room where the temperature \({\bf{75}}\;^\circ {\bf{F}}\). The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.

Each limit represents the derivative of some function f at some number a. State such an f and a in each case.

\(\mathop {{\bf{lim}}}\limits_{h \to {\bf{0}}} \frac{{\sqrt {{\bf{9}} + h} - {\bf{3}}}}{h}\)

19-32: Prove the statement using the \(\varepsilon ,\delta \) definition of a limit.

28. \(\mathop {\lim }\limits_{x \to - {6^ + }} \sqrt(8){{6 + x}} = 0\)

Find an equation of the tangent line to the graph of \(y = B\left( x \right)\)at\(x = 6\),if\(B\left( {\bf{6}} \right) = {\bf{0}}\),and \(B'\left( 6 \right) = - \frac{1}{2}\).

Which of the following functions \(f\) has a removable discontinuity at \(a\)? If the discontinuity is removable, find a function \(g\) that agrees with \(f\) for \(x \ne a\)and is continuous at \(a\).

(a) \(f\left( x \right) = \frac{{{x^4} - 1}}{{x - 1}},a = 1\)

(b) \(f\left( x \right) = \frac{{{x^3} - {x^2} - 2x}}{{x - 2}},a = 2\)

(c)\(f\left( x \right) = \left [{\sin x} \right],a = \pi \)
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