80246 If \(f(x)\left\{\begin{array}{cc}a x+b \text { if } x \leq 1 \\ a x^{2}+c \text { if } 1\lt x \leq 2 \\ \frac{d x^{2}+1}{x} \text { if } x \geq 2\end{array}\right.\) is differentiable on \(R\), then \(a d-b c=\)

80247 If \(f\) is defined and continuous on \([3,5]\) and \(f\) is differentiable at \(\mathrm{x}=4\) and \(f^{\prime}(4)=6\) then the value of \(\lim _{x \rightarrow 0} \frac{f(4+x)-f(4-x)}{4 x}\) is equal to

80248 Let \(g:[-2,2] \rightarrow \mathbb{R}\) and \(f:[-2,2] \rightarrow \mathbb{R}\)
Are two functions defined as
\(g(x)=\left\{\begin{array}{ll}-1 \text { if }-2 \leq x\lt 0 \\ x^{2}-1, \text { if } 0 \leq x \leq 2\end{array}\right.\) and
\(\mathbf{f}(\mathbf{x})=|\mathbf{g}(\mathbf{x})|+\mathbf{g}(|\mathbf{x}|)+2\). In the interval
\((-2,2), f\) is not differentiable at \(x=\)

80195 The function \(f(x)=[x]\), where \([x]\) denotes greatest integer function is continuous at

80246 If \(f(x)\left\{\begin{array}{cc}a x+b \text { if } x \leq 1 \\ a x^{2}+c \text { if } 1\lt x \leq 2 \\ \frac{d x^{2}+1}{x} \text { if } x \geq 2\end{array}\right.\) is differentiable on \(R\), then \(a d-b c=\)

80247 If \(f\) is defined and continuous on \([3,5]\) and \(f\) is differentiable at \(\mathrm{x}=4\) and \(f^{\prime}(4)=6\) then the value of \(\lim _{x \rightarrow 0} \frac{f(4+x)-f(4-x)}{4 x}\) is equal to

80248 Let \(g:[-2,2] \rightarrow \mathbb{R}\) and \(f:[-2,2] \rightarrow \mathbb{R}\)
Are two functions defined as
\(g(x)=\left\{\begin{array}{ll}-1 \text { if }-2 \leq x\lt 0 \\ x^{2}-1, \text { if } 0 \leq x \leq 2\end{array}\right.\) and
\(\mathbf{f}(\mathbf{x})=|\mathbf{g}(\mathbf{x})|+\mathbf{g}(|\mathbf{x}|)+2\). In the interval
\((-2,2), f\) is not differentiable at \(x=\)

80195 The function \(f(x)=[x]\), where \([x]\) denotes greatest integer function is continuous at

80246 If \(f(x)\left\{\begin{array}{cc}a x+b \text { if } x \leq 1 \\ a x^{2}+c \text { if } 1\lt x \leq 2 \\ \frac{d x^{2}+1}{x} \text { if } x \geq 2\end{array}\right.\) is differentiable on \(R\), then \(a d-b c=\)

80247 If \(f\) is defined and continuous on \([3,5]\) and \(f\) is differentiable at \(\mathrm{x}=4\) and \(f^{\prime}(4)=6\) then the value of \(\lim _{x \rightarrow 0} \frac{f(4+x)-f(4-x)}{4 x}\) is equal to

80248 Let \(g:[-2,2] \rightarrow \mathbb{R}\) and \(f:[-2,2] \rightarrow \mathbb{R}\)
Are two functions defined as
\(g(x)=\left\{\begin{array}{ll}-1 \text { if }-2 \leq x\lt 0 \\ x^{2}-1, \text { if } 0 \leq x \leq 2\end{array}\right.\) and
\(\mathbf{f}(\mathbf{x})=|\mathbf{g}(\mathbf{x})|+\mathbf{g}(|\mathbf{x}|)+2\). In the interval
\((-2,2), f\) is not differentiable at \(x=\)

80195 The function \(f(x)=[x]\), where \([x]\) denotes greatest integer function is continuous at

80246 If \(f(x)\left\{\begin{array}{cc}a x+b \text { if } x \leq 1 \\ a x^{2}+c \text { if } 1\lt x \leq 2 \\ \frac{d x^{2}+1}{x} \text { if } x \geq 2\end{array}\right.\) is differentiable on \(R\), then \(a d-b c=\)

80247 If \(f\) is defined and continuous on \([3,5]\) and \(f\) is differentiable at \(\mathrm{x}=4\) and \(f^{\prime}(4)=6\) then the value of \(\lim _{x \rightarrow 0} \frac{f(4+x)-f(4-x)}{4 x}\) is equal to

80248 Let \(g:[-2,2] \rightarrow \mathbb{R}\) and \(f:[-2,2] \rightarrow \mathbb{R}\)
Are two functions defined as
\(g(x)=\left\{\begin{array}{ll}-1 \text { if }-2 \leq x\lt 0 \\ x^{2}-1, \text { if } 0 \leq x \leq 2\end{array}\right.\) and
\(\mathbf{f}(\mathbf{x})=|\mathbf{g}(\mathbf{x})|+\mathbf{g}(|\mathbf{x}|)+2\). In the interval
\((-2,2), f\) is not differentiable at \(x=\)

80195 The function \(f(x)=[x]\), where \([x]\) denotes greatest integer function is continuous at