Please help me with this question. == andLet f(x)if x > 0g(x)18 +if x < 0Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f -g is constant?If f'(x) = g'(x) for all x in an interval (a, b), then f- g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.For x > 0, f(x) = g(x), so f'(x) = g'(x). For x < 0, f'(x) =and g'(x) =so f'(x) ? g'(x).However, the domain of g(x) is not an interval [it is (-o, 0) U (0, 0)] so we cannot conclude that f- g is constant (in fact it isnot).Need Help?Read ItWatch It

Name: Please help me with this question. == andLet f(x)if x > 0g(x)18 +if x
Uploaded: 2024-03-20T07:06:27.000Z
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Description: Please help me with this question. == andLet f(x)if x > 0g(x)18 +if x < 0Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f -g is constant?If f'(x) = g'(x) for all x in an interval (a, b), then f- g is

Given,The function g(x)=1x Consider only the case when x<0 because already know that f(x)=g(x) when x>0. When x<0,The function f(x) and g(x) are not equal but their derivative must be equal. f'(x)=g'(x) In the function of gx=8+1x Since'8' is constant and it is added to the term,so derivative of constant will be zero.Then first derivative of g(x) is equal for all x in their domain. And f(x)-g(x)=1x-8+1x=-8 So it is clear that f-g is a constant.