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Let f : R to R and g: R to R be , respe...

Let `f : R to R and g: R to R` be , respectively, given by `f(x) = |x|+1 and g(x) = x^(2) +1`. Define `h: R to R ` by `h(x) = {{:(max. {f(x),g(x)}",",,"if"x le 0 ), ( min. {f(x), g(x)}",",, "if"x gt 0):}`
The number of points at which `h(x)` is not differentiable is ________.

Text Solution

Verified by Experts

The correct Answer is:
3
PLAM
(i) In these type of questions, we draw the graph of the function.
(ii) The points at which the curve taken a sharp turn. Are the points of non-differentiability.
Curve of f (x) and g (x) are

h (x) is not differentiable at `x = pm 1 and 0`.
As, h(x) take sharp turns at ` x = pm 1 and 0`.
Hence, number of points of non-differentiability of h (x) is 3.
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