• Let a) f: IR₁ ->R₂ & f(x) = - = b.) f: IR₁ → IR₂ & f(x) = 2x² +7 EXC 3X 3 2 Do some appropriate restrictions on RT & R₂ (if necessary) to make of ? one-to-one & Onto. After which, solve. for f- & show that fof- & f of are all equal to the s identity function. 8x8 2x01

Q: Let f(x)=xsinx+V1-x Evaluate f'(-). Select one: а. 2 b. 0 C. d. 3

A: According to product rule of differentiation and according to power rule of differentiation .

Q: a) Find 2 x-intercepts of the function f (x) = a² + 6x . The x-intercepts are and (write smaller…

A: a) The x-intercepts of a function is the points where the graph crosses x-axis . The values of y…

Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

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Q: Find f'(x) for each of the following:< Ax) = 3x³ – 2x +4 b Ах) — 3(х + 2)? -2е a 8x* – 3x Ax) = Ax)…

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Q: Differentiate 3x-1 2x + 3 with respect to 'x'.

A:

Q: Find: te (1 + Inx + ) he y? y+ylnx+ 2x O ylnx +y o 1 y x2 « Previous 98 %23 立

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Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x&gt;0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: et f(x) = x³ + 4x. Using fact that f(2) = 16 find (f-1)'(16)

A: Topic:- application of derivatives

Q: If f(x) = Vx +1 , g(x) = Vx – 1, find the domain of f +g. %3D

A: Domain is set where function is defined

Q: Use the proper manipulation, differentiation and/or integration of the power series for f(x) to find…

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Q: 4x - 7x Differentiate with respect to 'x' 6x + 5

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Q: Let f(x)= ax'+x² + bx +6 where a and b are real numbers, and f(2)=3. Find the value of f(-2).

A: f(-2) = 17  The detailed solution is as follows below:

Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

A:

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? a. Concave upward on (-1, o0)…

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Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: Find ao of the function f(x) =÷(n - x)2 | О п^2/12 5 T^2/6 5 T^2/12 O T^2/6

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Q: Let f(x, Evaluate f(3, 4) y)=√150 - 4x² - 2y²

A: fx, y=150-4x2-2y2

Q: (х, у) — ху? + yex- +5

A: we have to find fxx and fyy.

Q: Compute for the possible root of the function f(x) = x4 - x³ - x? - 4 in the interval [-2, -1]. Use…

A: The equation in the form f(x)=0 is called a transcendental equation. If the function is continuous…

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: 2. In the following function, determine f'(x): 2 a. 3√√x2 b. 15x4 C. 1 2 x² +6 x3 20x320 2

A: NOTE: As per the guidelines, I have solved three parts. If  you want solution of the remaining part,…

Q: The derivative of the function In In(coth a? – 1) is

A: follow next step