ists for all z € I (but f' need not itself be continuous). Suppose further at f'(a) < f'(b). Prove for any y with f'(a) < y < f'(b) that there is me ce I such that f'(c) = y.

Q: These are true or false questions

A: 3) If f(x) is differentiable at any point x=a, then it must be continuous at x=a So the given…

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A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: Let f(x) = (a) f(1) = (b) f'(6) = 2x³ - 5x² x2 Evaluate f'(x) at the following points:

A: f(x)=2x3-5x2x23xba=xbad dx(x)m=mxm-1

Q: Draw a graph for following f' > 0 on (-∞,1) and f"l > 0 on (-∞, 1) U (1, ∞).

A:

Q: Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15]. Compare each…

A: 1) &gt; left sum will be greater than right because function is decreasing 2)  &lt; because…

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A:

Q: Prove f-1(E U F) = f-\(E) U f-1(F)

A: We have to prove that f−1E∪F=f−1E∪f−1F. Let x∈f−1E∪F hence, x∈f−1E∪F⇔fx∈E∪F…

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A:

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

A: If the first derivative of a function is negative then the function is decreasing and vice versa.…

Q: Let f(x) = ()*)**, x = 0,1, is p.d.f then P(x = 0) = %3D

A:

Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

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A: Here we need to show the way to prove a∈f-1(Y)

Q: Suppose f" () > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: Step 1: Let write the given .We are given that f"(x)&gt;0 on some interval (a,b). Step 2: Let write…

Q: 83. Let f(x) = In (1 – x²). (a) State the domain of f. (b) Find f'(x). (c) State the domain of f'.…

A: Since you have asked multiple question and have not specified any question in particular, I will…

Q: Suppose that a function h satisfies −x^2 ≤ h(x) ≤ x^2 for all x. Prove that h is differentiable at x…

A:

Q: Please just do 1(b)

A: To compute the required value , by definite integral

Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

A:

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A:

Q: if f'(a) exists, then f is continuous at x = a. True False

A: Function f differentiable at x=a

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A:

Q: Are there independent linear functions with derivative number n – 1 continuous 91 ,..., „,with…

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Q: Q7/ * find f`(2/3), where f(x) =x tan-'(x/2) T/3+v3/4 O H/3+v3/4 O T/3+v(3/4)

A:

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

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Q: Let F (x) : tan't dt. Find F' (V3 -1, 4 27

A: