Let f : R → R and g : R → R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R → R by h x = max ⁡ f x , g x i f x ≤ 0 min ⁡ f x , g x i f x > 0 Then number of points at which h x is

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Let f : R &#8594; R and g : R &#8594; R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R &#8594; R by h x = max &#8289; f x , g x i f x &#8804; 0 min &#8289; f x , g x i f x &#62; 0 Then number of points at which h x is not differentiable is_________

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h x = x 2 + 1 , x ∈ - ∞ , - 1 - x + 1 , x ∈ - 1 , 0 x 2 + 1 , x ∈ 0 , 1 x + 1 , x ∈ 1 , ∞ Hence, not differentiable at x = - 1 , 0 , 1

Let f : R → R and g : R → R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R → R by h x = max ⁡ f x , g x i f x ≤ 0 min ⁡ f x , g x i f x > 0 Then number of points at which h x is not differentiable is_________

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Step-by-step solution

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Let f : R &#8594; R and g : R &#8594; R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R &#8594; R by h x = max &#8289; f x , g x i f x &#8804; 0 min &#8289; f x , g x i f x &#62; 0 Then number of points at which h x is not differentiable is_________

Correct answer

Step-by-step solution

More from Continuity and Differentiability

Let f : R → R and g : R → R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h : R → R by h x = max ⁡ f x , g x i f x ≤ 0 min ⁡ f x , g x i f x > 0 Then number of points at which h x is not differentiable is_________