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Chapter 2: Q43E (page 77)

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

Short Answer

Expert verified

The numbers at which \(f\) is not differentiable are \(x = 1\) and \(x = 5\).

Step by step solution

01

Differentiability of the Function

The function is a differentiable function whenever the derivatives of that given particular function seem to exist at any particular point within the interval of convergence.

02

Find the numbers at which the function is not differentiable.

The given graph is:

Clearly, at\(x = 1\), the derivative of the curve cannot be defined, so differentiability is undefined. And at \(x = 5\), the function is having vertical tangent.

Hence, the numbers at which \(f\) is not differentiable are\(x = 1\) and \(x = 5\).

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Most popular questions from this chapter

\({x^{\rm{2}}} + {y^{\rm{2}}} = ax\), \({x^{\rm{2}}} + {y^{\rm{2}}} = by\).

41-42 Show that f is continuous on \(\left( { - \infty ,\infty } \right)\).

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(a) The van der Waals equation for \({\rm{n}}\) moles of a gas is \(\left( {P + \frac{{{n^{\rm{2}}}a}}{{{V^{\rm{2}}}}}} \right)\left( {V - nb} \right) = nRT\) where \(P\)is the pressure,\(V\) is the volume, and\(T\) is the temperature of the gas. The constant\(R\) is the universal gas constant and\(a\)and\(b\)are positive constants that are characteristic of a particular gas. If \(T\) remains constant, use implicit differentiation to find\(\frac{{dV}}{{dP}}\).

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