Find a number a in [0, 1] such that f (a) = fave over the interval [0, 1]: f(x) = 3x² O الله O √3 O الله O 13 3

Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

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Q: X4 none of these X (c) f'(x) does not exist.

A: f''(x) = 0  at sharp corner f'(x) does not exist for f'(x) = 0 , tangent line is horizontal

Q: Show that the set of functions 1,cosx,sinx,cos2x,sin2x,…,cosmx,sinmx,… is orthogonal on the interval…

A: We are given the following functions: 1, cosx, sinx, cos2x, sin2x,…, cosmx, sinmx, …   Our aim is to…

Q: 6. Prove that |xy| = |x|ly| for all real numbers x, y.

A: The given problem is to prove the following statement. Given statement is |xy|=|x||y| for all real…

Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

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Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i>j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Let f(x) = x³ - 10, x= [-15√3, 15√3]. Find the value of c guaranteed by the Mean Value Theorem on…

A: The given function fx=x3-10, x∈-153, 153. We have to find the value of c guaranteed by the Mean…

Q: The floor function is defined as bxc = max{m ∈ Z | m ≤ x}. Effectively, the floor function is the…

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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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