Let f(x) = and I =]1, 00[. Then for all x, y > 1, -1 3+Vx X-y is less than 1/64 None of these is less than 1/144 is greater than 1/64 is equal 1/64

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Q: for the function f(x) = x^3 − 2x^2 + 4x − 8 on the interval [1, 6]

A: Mean value Theorem:-Statement: Let f be continuous over the closed interval [a, b] and…

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A: We have to find the derivative for each of the functions. 1. fx=x2+lnxx3+4x+52. f(x)=x2+5xlnxx-6xex

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A: I am attaching image so that you understand each and every step.

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Q: 6. y = xe* 7. y= 3x.e* 8. y = x² In(x) 9. y =x*(5x – 1) 10. y = (x² + 2x)5(3x-3 +x²)-7 11. y = (1 –…

A: Use product rule of differentiation.

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

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Q: 4 If f(x) = ln(2x² – 3) then f'(x) =? - 2x a) 2x2 – 3 - 4x b) 2x2 – 3 2x c) 2x2 + 3 -4x 2x2 – 3 -…

A: f(x) = ln(2x² - 3) So, f'(x) = 1/(2x²-3) × (2x²-3)' So, f'(x) = 4x/(2x² - 3) .... Option (b)

Q: ! Given f (x) = {x + 2 if x > 10 lx – 7 if x < 10' D. ! determine each of the following. a.) f(14)…

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Q: If f(4) 8 and f '(x) 2 1 for 4 < x < 9, how small can f(9) possibly be?

A: Given:- If f(4) = 8 and f '(x) &gt; 1 for 4 ≤ x ≤ 9 To find:- How small can f(9) possibly be?

Q: Let 11 f(x) dx = 9, 10 Find "f(e) de = [ and nd S 9f(x) - 7 dx 10 [₁ f(x) dx = 7, [1² f(x) dx = 9.…

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Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

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Q: If f(3) = 5 and f'(x) ≥ 3 for 3 ≤ x ≤ 6, how small can f(6) possibly be? f(6) ≥

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Q: Let ˜(x)=3e³x (10−6x)+e³* (−6) Find the value of x that makes f(x) = 0 Pick test values and plug in…

A: Topic:- function

Q: Simplify f(x) = f'(x)= = (1³2²) ² f(x)= Use this result to find the derviative of f(x).

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Q: Find y" y=    __1 +x__          1 −x

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.