4. Suppose that f and g are continuous on the closed interval [a,b] and dif- ferentiable on the open interval (a,b). Suppose also that f(a) = g(a) and f'(x) < g'(x) for a < x < b. Prove that f(b) < g(b).

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Q: Suppose you know that the function f is decreasing and concave down on t interval [2, 7]. which of…

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Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: Let f be a function that is continuous on [1,7] and differentiable on (1,7). Suppose 2 < f'(x) < 3…

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Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

A: The graph of continuous function f(x) is given in the options. The given data of the function f(x)…

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Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: each

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.