The critical points of the function f(x) = 9x? – 2x occur at %3D O r = 0, r = +2.00 O z = 0, x = ±1.50 O a = 0, x = ±1.20 O r = 0, x = +6.00 O z = 0, x = ±0.75 %3D %3D %3D

Q: If F(x) = f(g(x)), where f( – 4) = 9, f'(– 4) = 6, ƒ' (2) = 1, g(2) = – 4, and g'(2) = 8, find…

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Q: Verify that g'(x) 1 where g(x) = v2x – 3. %3D V2r – 3

A: Giveng(x)=2x-3.To verify g'(x)=12x-3  is the derivative of g(x).

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: Compute the second order derivative f"(x) for f(x) = 3x* -/x. %3D 36x2- 4x2 Ob.36x2 + 3/2 3/2 1 OC.…

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Q: If f(x) = sin x 7T find f %3D (a) 1 (b) / 2 2. . т (c) 1– 4 (d) V2 1+ (e) /2 (1- 3)

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Q: Use the table below to compute h'(2) for h(x) = 2 + 2g(x). f(1) g(x) f'(x) | g'(x) 0. 0. -2 2 1/2 -3…

A: Given query is to find the derivative of h(x) at x=2, from the given table.

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Given: Function, f(x)=150-15x           Boundary conditions: u0,t=u3,t=0To find: ux,t, u42, 0.1

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

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Q: 1-cos2x/1+sinx=sinx. Prove the identity

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Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: f (x) = 5.6 sin (2.6x – 4.2) – 9.1- What is the equation of the midline of the function %3D o y =…

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Q: Differentiate the given function: g(x) = sec¯ ec- (x²) ...

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Q: After the function f (z) was carefully differentiated, the function f'(z) = 5- In(2) - 2 resulted.…

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Q: (D) h(x) = 12g(x) – 11f(x). | h'(2) = (E) h(x) = 10f(x) + 9g(x) – 2. %3D h'(2) = (F) h(x) = –10g(x)…

A: Given that :- f'2=-6g'2=9h'2=?

Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: 1. Which of the following are one-to-one functions? (Choose all that apply.) a) f(x) = x? b) f(x) =…

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Q: ) Given f'(x)=12.r -4r+8, and f (3) = 1000 find f.

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(5) = 11, f(11) = 3, f'(11) = 6, f'(5) =…

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Q: Let z = x"y . If x increases by 2% and y increases by 3% then using partial differentiation theory…

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Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

Q: Suppose that f'(x) = 3x² + 3 – 1 and f(1) = 3. Find a formula for f(x) and then %3D %3D use this…

A: Topic- integration

Q: Let P(x) = F(x)G(x) and Q(x) , where F and G are the functions whose graphs are shown. G(x)' F 4 2 G…

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Q: Consider the function f(x), whose first and second derivatives are given below: 26 8x27 208x(x-54) =…

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Q: 10) Given f'(x) = 3x+ 2x + 1 and f(1) 4, determine ƒ(x). %3D %3D

A: Given f'(x)=3x²+2x+1....(i) and f(1)= 4...(ii)

Q: If f(z) = 8 tan z, then find the value of f'(3) is %3D V10 3 10 10 3 10

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Q: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

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Q: If f(x) = csc(3x). then f' (x) = %3D o -3csc(3x)cot(3x) o -3csc2 (3x) o 3sec(3x)tan(3x) o 3tan? (3x)

A: Given: fx=csc3x To evaluate: f'(x)