f(x) = x2 − 4|x| and g(x) = {min{f(t) : −6 ≤ t ≤ x},

Discussion Forum : Application Of Derivatives

Question -

$f (x) = x^{2} - 4 | x | a n d g (x) = {\begin{matrix} m i n {f (t) : - 6 \leq t \leq x}, x ϵ [- 6, 0] m a x {f (t) : 0 \leq t \leq x}, x ϵ [0, 6] \end{matrix}, t h a n g (x)$

Options:

A . Exactly one point of local minima

B . Exactly one point of local maxima

C . No point of local maxima but exactly one point of local minima

D . Neither a point of local maxima nor minima

Answer: Option D
:
D

Bold line represents the graph of y = g(x) clearly g(x) has neither a point of local maxima nor a point of local minima.

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