Where the function f(x) = |x| is differentiable? Discuss. A farmer has | Mathematics I 2081

Mathematics I208110 marksNumerical: differentiability and optimizationDifferentiability of a function

Where the function $f(x) = |x|$ is differentiable? Discuss.

A farmer has 1200 m. of fencing and wants to fence off a rectangular field that borders a straight river. He needs to fence along the river. What are the dimensions of the field that has the largest area? [5+5]

Where the function $f(x) = |x|$ is differentiable? Discuss.

(a) Differentiability of f(x) = x - Function: $f(x) = x$ $f$ is differentiable at $a$ if the limit below exists: $f'(a) = \lim{h \to 0} \frac{f(a+h) - f(a)}{h}$ $f(x) = x = \begin{cases} x & x \geq 0 \\ -x & x < 0 \end{cases}$ $f(x) = x \Rightarrow f'(x) = 1$ . Differentiable.

(a) Differentiability of f(x) = x - Function: $f(x) = x$ $f$ is differentiable at $a$ if the limit below exists: $$f'(a) = \lim{h \to 0} \frac{f(a+h) - f(a)}{h}$$ $$f(x) = x = \begin{cases} x & x \geq 0 \ -x & x < 0 \end{cases}$$ $f(x) = x \Rightarrow f'(x) = 1$. Differentiable.

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Where the function f(x) = |x| is differentiable? Discuss. A farmer has 1200 m. of fencing and wants to fence off a rectangular field that borders a straight river. He needs to fence along the river. What are the dimensions of the field that has the largest area? [5+5]