10. Consider the function f(x) = x³ + 2x² + 10x - 20 = 0 1. Show that f(x) has one single root in the interval ]1,2[ 2. Show that this function can be put into the form: x= F(x) = z²+bx+c 3. Show that for a root in the interval re [1, 2]: F'(r)| ≤ //

Q: MTH 32 (16) Show that f is one-to-onc. Find (f-¹)'(a). Calculate f-¹. Find the domain and range for…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the function below f(x) = 3 x³ – ²x² − 18 x + 3 a) Differentiate the functionƒ(x) = 3 x³ − 2…

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Q: A function f(x) has an inflection point at (2,-2). Which of the following could NOT have been the…

A: We know that point of inflection can occur where the second derivative is 0. It is the point at…

Q: 2. a. f(x) = (x+2)/(x +4). Use the Mean Value Theorem on the interval [0, 4] to find all values of x…

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Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

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Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x>0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

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Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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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: When z = f(x,y), which of the following is true for the whole statement? O ddz = f"(x).dx² and dx2…

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Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Find numbers a and b so that f'(1) exists for ax² + b 1 x² f(x) = if if x 1.

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Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

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

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Q: function of xx if

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Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: Let f be the function given by f(x) = 4x³ - 5x² + 6x + 7. What is the value of f'(-1)? 28 O 12 CO

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Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: 3. Let f(x) = 4x3+ + 2vx-7. Find f'(x).

A:

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

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Q: Q6. Verify that 8²1 əxəy for the function f(x,y) = ln(2x + 3y)

A: Given,            fx,y=ln2x+3yTo find : Verify that ∂f∂x∂y for the given function.

Q: Let f(x) = -2x√√x + f'(x) = -8 x²√x

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Q: Differentiate f(x) = Vx² + 1(³. Do not simplify. x+2"

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Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

A: