(i) Use the IVT to show that there is some number t in (1, 2) such that 3(t? +1)? = 20t. 1. Use part (i) to verify the Mean Value Theorem for 1 f(x) = a = 1,6 = 2. x² + 1'

Q: The average value of f(x) = 2x³ 14x? on the interval [-1, 7] is |

A:

Q: Suppose f"(x) = (x + 2)°(x + 1)²(x – 2). Which of the following statements about the curv y = f(x)…

A: If f"(x) > 0 , curve is concave up If f"(x) < 0 , curve is concave down So only check the sign…

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Q: 28. Let f be the function given by f(x) = 2 cos x + 3e. What is the value of f'(0) ? (A) -3 (B) 0 3…

A:

Q: Consider the given function and the given interval. f(x) = (x − 6)2,    [4, 7] (a) Find the…

A: Given information:The given function is

Q: 2a) Use integration to find the average value of the function f(x)=x(4-x) over the interval [0,4].…

A:

Q: What is the range of the function f(x) = 23 sin 4x+1 ? A B [0, ∞) D [4,16] C) [1,4] [2,00)

A: Range is the set of y values corresponding to x values of domain.

Q: 2(x²+4) Find the average value of f(x) = x2 on the interval [1, 3]. 8 3 28 3 O 12 14 3 O 14

A: Average value of a function is ratio of difference in outputs and difference in inputs.

Q: 1) Find the average value of the function f(x) = 3-4x + 5x² over the interval [-1, 3].

A: The function is given by fx = 3-4x+5x2 To determine: The average value of the function over interval…

Q: The average value of the function f(x)=x²-19 on [0,9] is

A:

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Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

A: