Suppose f: (0,00) → (0, ∞) and g: (0, ∞o) → (0, ∞o) are continuous functions. True or false: If g and fog are differentiable, then f must be differentiable too. True False

Q: If f(x) = g(x) for x # c and f(c) # g(c) then either f or g is not continuous at c.

A: Continuous Function:In mathematics, a continuous function means that a continuous change in the…

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: Suppose f: (a, b) →→ R is differentiable. True or false: If f is unbounded, then f' (the derivative…

A: f:a, b→ℝ is differentiable.

Q: Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point…

A: Consider the conditions for the mean value theorem.

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: 3. Determine whether f is differentiable or not differentiable at 1. (x – 1 if x > 1 (-x² _if x <1…

A: If a function is differentiable at any point x=a ,then its L.H.D. =R.H.D.

Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

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Q: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: Suppose that f(a) = f(b) = 0 and the second derivatives of f exist on the closed interval [a, b].…

A: Prove that ∫abx-ax-bf"xdx=2∫abfxdx.