(a) (b) Suppose f() is convex on the interval [a,y] CR, and there's a point 3 such that a

Q: Let f(x) = {ax² (2x + b differentiable (a) 1 at x = 1. x ≤ 1 x>1 (b)-1 . Find a so that f is (c) 2…

A: Here is the solution:

Q: If f(x) =-3x, Show that f (x) satisfies the hypothesis of the Roll's Theorem on the interval [-3, 3]

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Q: (1) The domain of the function f(x, y) is the set: y+1 (a){(x, y)– 2sxs2,y # -1} (d){(x, y)| –…

A: Explanation of the answer is as follows

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

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Q: The function f has continuous second derivatives, and a critical point at (-8, -7). Suppose frz(-8,…

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Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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Q: The domain of

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Q: The function f(x) = 6e-2x is concave upward over the interval: a b C Od (1, +∞0) (-∞, +∞0) (-∞0, 0)…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: 3 a) Let f(x) = x(x + 4) ³. The only inflection point of f(x) which lies in the interval [-2/2,0]…

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Q: 3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the…

A: The answer to this question is given below.Explanation:

Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

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Q: Determine the interval(s) over which f(x) = (x − 4)³ is concave downward. O a O b Od (-∞0, 4) (-∞,…

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Q: 2х f(x) = ,x 1

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Q: Show that the given function is not analytic at any point but is differentiable along the indicated…

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Q: f : R --> R is defined by f(x) = 2x+1, A= (0,1)  and B = [ -1,1 ]    find f [A] and f-1[B]

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Q: The set of all points where the function f(x) = i-e¨ is differentiable is (A) (0 , ∞) (B) ( –0, ∞)…

A: We find the set of all points where the given function f(x) is differentiable.

Q: i) Show that f(Z) = 7x – 6iy is nowhere differentiable. ii) Determine whether the following function…

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Q: 1) Find the absolute maximum and absolute minimum for f(x) = x-3x-2 on the closed interval [-2, 11.

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Q: Let f (x)- - 6x² + 9x – 8. The absolute maximum of f(x) on the closed interval [0,5] is (1,4) This…

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