|a| x2 – 1 Determine all points at which g(x) is differentiable. Justify your answer.

Q: If f and g are differentiable at a , then f (x) + 4g (x) = I (x) + g (x)]. True False

A: Here, the given statement is  If f and g are differentiable at a, then ddxf(x)+ddxg(x)=ddxf(x)+g(x)

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D ...

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Q: Let f(x) = ax + bx . If (1,6) is a relative extremum point, then b is? %3D

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Q: Find the local linearization of f(x) = x2 at 2. L>(x) = Submit answer

A: Ans.  =4x-4  For detail...go through the solution, I have done step by step

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: Let f(x)=x2+2x. Find all values of c in the interval [−2,0] such that f′(c)=0.

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Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: [x² when x # 1 9: Show that f(x) = %3D 2 when x =1 is discontinuous at x = 3D1

A: The given function is: f(x)=x2when x≠12when x=1We have to show that the given function is…

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: Q.1 A-Find and sketch the natural domain of f(x, y, z) In(2-x2-y2)

A: You have ask multiple  questions  but not specifiy any particular  questions  so , according to…

Q: The function f(x) (x2 -1)3, is increasing on the interval (-00,-2)U(0,2) .A (-1,0) U (1, 0 ) .B

A: The given function is f(x)=(x2-1)23

Q: Q.59 Consider the function f(x) = x² – x - 2. The maximum value of f(x) in the closed interval [-4,…

A: We know that  Second Derivative Test To Find Maximum &amp; Minimum Let us consider a function f…

Q: f(x, y) = In(3 - x) √x² + y² = 8 - a) Find the domain of the function b) Sketch the Domain

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Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D

A: Given f(x)=ax4+bx

Q: of and ду of Consider the function f(x,y) = 9x' - 4y - 2. Find -

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Q: Find the value of c in the interval (a,b) such that f'(c)=0 for f(x)=(x-3)(x+1)´ on[[-1,3].

A: the value of c is:-

Q: 2. Find whether the function F = (x -y')i+ – 3x)7+(z² - xy )k i %3D

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Q: Find numbers a and b such that the given functiong is differentiable at 1. |ax³ - 3x if x 1 a = b =

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Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

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Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

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Q: (f) The function f(x) = √√x is differentiable at x = 0. ○ True O False

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: b): Apply Rolle's theorem for the function f(x) = x² + 4x over the interval -4,0]. Justify your…

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Q: - (i) Determine whether the function f: R - R, f(x) = X+1 x*3 is surjective. x-3"

A: As you post multiple questions According to guidelines I only solve the first one.

Q: Prove from the definition of differentiability that the function f : R\{3/2} → R f(x) = 3 – 2x is…

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Q: Given F(x) = °2 (1 –V1 - (1+ 1)² ) Evaluate F(0) and F'(V2) using the First Fundamental Theorem of…

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Q: Find the constant a such that the function is continuous on the entire real line. (sx, lax 9₁ a=…

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Q: Consider the function f(z) = (a+ 1) x²y² + i(3 + 1)x²y?. Determine at which points the function f(z)…

A: Answer

Q: .a Is the function a.EVEN b. ODD f(x) = |x|, π<x< T

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Q: Find a and b so that the function f(x) = S 4x – 7x² + 5, a -2 is both continuous and…

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Q: The function f(x) = 7 is differentiable everywhere. %3D O True O False

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

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Q: The position of a mysterious object in space is represented by the given function f(x, y) = 2x² +…

A: differentiate the given function with respect to x and y partially ∂f∂x=4x+2y+0+2 =0 ∂f∂y=0+2x+2y+0…

Q: The domain of f(x) = /1 – I In(x) is %3D

A: The domain is the set of all possible x-values which will make the function give real y-values as…

Q: Consider the differentiable functionf with f(4) =; and f'(4) = If g(x) = f(x²), then gʻ(2) = А. 1 B.…

A: Given : f(4) = 1/2 f'(4) = 1/3 g(x) = f(x2) Find g'(2) = ? g(x) = f(x2)          (given)…

Q: Use a formula to express y as a function of t if  y = 3x2 + 9x and x = t − 1.   y =

A: First of all, both equations i.e. y in terms of x and x in terms of t.

Q: Show that the function f(2) = xy| is not analytic at the origin, even though C.R. equations are…

A: It is given that the function fz=xy. To check the function f is differentiable at z=0.…

Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

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Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: By first fundamental theorem of Calculus if f (x) = V19 +t²dt then f'(3) is? %3D

A: Given f(x)=∫0x219+t2dt

Q: Show the function f(z) = 1+2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Find a and b so that the function 7x3 – 3x? + 8, x -2 f(x) = ax + b, is both continuous and…

A: To Determine: find a and b if f(x) is both continuous and differentiable. Given: we have…

Q: (b): Apply Rolle's theorem for the function f(x) = x² + 3x over the interval [-3,0]. Justify your…

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Q: Q3) Let f(z) = 4y + x³ + i(y³ – 4x) a) Determine where the function f(z) is differentiable b)…

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Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

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Q: Find the value of c in the interval (a, b) such that f'(c) = 0 for f(x) = (x – 3)(x + 1)? on [-1,3].

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