If f(x) is continuous on the interval [a, b] and a

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: Prove that if f is a continuous function on a closed interval [a, b], then

A: We have to prove the given inequality for a continuous function on a closed interval [a,b].

Q: X +5 ×ラン2x?+x メP

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Q: Let Ax) = 2x - 7x +4x. %3D a. On what interval(s) is f'(x) > 0? b. On what interval(s) is fx)…

A: Given: fx=2x3-7x2+4x   The Power law: ddxxn=nxn-1

Q: if f(x) is continuous on [a, b], then we can always say that: Select one: O True O False a b a…

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Q: ,if x>2 Find the correct value of bb that makes

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Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: If f is continuous, then b+c f(x)dx = ] -S Fx - c)dx f(x – a+c

A: Translation along the horizontal axis can be obtained using the transformation rule x→x-a on the…

Q: Apply the Mean Value Theorem to f on the indicated interval. Find all values f(b) – f(a) b- a f' (C)…

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Q: Determine the signs of f' and f" for each of the intervals. y = f(x) A Bc'D'E'F'G

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Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

A: If we have F(x)=∫0xf(t)dx then we have F'(x)=f(x). This is called the fundamental theorem of…

Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…

Q: Let f(æ) = /90 - x and g(x) = x² – a. Then the domain of f o gis equal to [a, b] for a = Preview and…

A: Given: fx=90-x, gx=x2-x

Q: The function f(x) = x² + 1 satisfies Rolle's Theorem in the interval [-2, –0.5]. - x² Select one: O…

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Q: Let f be a continuous function and a < b. Show that: b -a f(-x)dx = | f(x)dx a -b

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