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

A:

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A: here we have to find the value of Z after applying mean value theorem ,  the given function is…

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

A:

Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

A: Given: fx=5x2-4x+7 for x∈1, 4 To be find c∈1, 4 such that fc=13∫14fxdx Integral of ∫xndx is given by…

Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x^3…

A: Given : f(x)=x3+x-3  [0,2] The mean value theorem states that for a continuous and differentiable…

Q: 2. Determine whether the Mean Value Theorem applies for the function over the given interval.…

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Q: consider the ff. function: f(x, y) = cot" "^ (1+x) - 2x + ³y 3y 2e

A: Given the function             f(x, y)=cot-1(1+x)-2ex+3y Where              x=s2+t2,  and…

Q: VI. Let f(x)=x²-x²-x+1 on [-1,2]. Find all numbers c satisfying the conclusion to the Mean value…

A: Let fx=x3-x2-x+1 on -1, 2.To find all numbers c satisfying the conclusion to the Mean value theorem.…

Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: Use a linear approximation to estimate the value of sin 0.06. Verify that f(x) = satisfies the…

A: Use formula of linear approximation