Find local minimum value of the function f given by f(x) = 3+ | x |, x ∊ R.

Solution

f (x) = 3 + | x |, x ∊ R
f is not differentiable at x = 0
∴ 0 is a critical point of f.
Now, $straight f left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell 3 minus straight x comma space space space space space space space space space straight x less than 0 end cell row cell 3 plus straight x comma space space space space space space space space space straight x greater than 0 end cell end table close$
$therefore space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell negative 1 comma space space space space space space space space space straight x less than 0 end cell row cell 1 space space space space space space space space space space space space space space straight x greater than 0 end cell end table close therefore space space space space at space space space straight x space equals space 0 comma space space space space space space space straight f space apostrophe left parenthesis straight x right parenthesis space changes space from space minus ve space to space plus ve therefore space space space space space space straight x space equals space 0 space is space straight a space point space of space local space minima space of space straight f space and space local space minimum space value space of space straight f space equals space straight f left parenthesis 0 right parenthesis space equals space 3$

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Application Of Derivatives

Find local minimum value of the function f given by f(x) = 3+ | x |, x ∊ R.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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