Find all points on the graph of 3x² + 6y² + 3xy = 64 where the tangent line is horizontal. (Give your answer as a comma-separated list of points in the form (*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.)

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: Use logs and implicit differentiaton to prove (root(x))' = 0.5x^(-0.5)

A: Let y = √x Take log to the base e, i.e. natural log, i.e ln on both the sides, ln(y) = ln(√x) =…

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A: Given: (12,15)

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A:

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x2…

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Q: Please show step-by-step solution!

A:

Q: Use a linear approximation to approximate √48.

A: Here we have to find the square root of a number, so we take function f(x) = sqrt(x).   The linear…

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A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: find the slope of the tangent line to the graph of f at the given point f(x)=x^2-8x+2 at (2,-10)

A:

Q: Find an equation of the tangent line to the graph of f(x) = 4 - x2 at the point (-1,3).

A: Solve for the equation

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: Write cosh(In(x)) as a rational function of x.

A: write coshlnx as a rational function of x

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Q: Find the tangent line to the graph of f(x) = 3ex - 5x2 at x = 2.

A: A line is generally an object in geometry that doesn't bend i.e. it has no curve. It is a collection…

Q: Find the slope of the tangent line at (8, -8).

A: Given- Point 8,-8. To Find- The slope of the tangent line at the given point. Identity Used- tanθ=yx

Q: Find all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is…

A: The derivative of xn is nxn-1 for n≠0. The derivative of f(x)+g(x) is f'(x)+g'(x). The derivative of…

Q: Find the slope of the secant line in red.

A: Given that:

Q: 3) Use the Intermediate Value Theorur to show that there ís a root of the equation Make sure you…

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Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1]

A:

Q: Find all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is -5

A: Given: ƒ(x) = x3 + 9x2 + 19x - 10 The slope of the tangent line is -5

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A: use the tangent plane to estimate the value of √(4.8x5.02)

Q: Find the equation of th line perpendicular to the line 3y=2-4x and passing through the point (4,7)

A:

Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

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Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

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A:

Q: Write the equation of the tangent line to the graph ofy = (7x2 − 6x + 2)(1 + 2x)atx = 1.

A: we have to find tangent line to f(x) at x=1first we will compute tangent point at x=1

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A:

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A: This is a problem related to derivative. Based on the general formula and concept we will answer the…

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A: If the point on the curve h(x) = x2 − 8 is closest to the point (−18,−8), then their distance will…

Q: See image below.

A: We subtract x from both sides

Q: Locate the point where the slope of tangent line to y = In 2x2 is -1- 9. In 8. O (-2, In 8) In

A: Given that: y=ln 2x2

Q: Find the slope of the line tangent to the graph of the relation (5x - 34e)(y +5e) = e(x - 10e) at…

A: The given relation is, 5x-34e(y+5e)=e(x-10e) taking ln both sides,

Q: Find the equation of the line that is tanget to f(x)= sqrt(x+1) at the point (8,3).

A: The given function is

Q: Find the slope of a line that is tanget to f(x)= sqrt(x+1) at the point (8,3).

A: Given: The slope of the line at point (8,3) is given by

Q: Find the length of the curve on the interval 3/2 Y= (10x+ 15) 15

A:

Q: Find an equation of the tangent line to f at a = 9. (Express numbers in exact form. Use symbolic…

A: Topic:- limits and application of derivatives

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A:

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: By using formula of lenght of sub tangent and sub-normal

Q: Is the distance between any two different real numbersalways positive?

A: State whether the distance between any two different real numbersalways positive or not

Q: Express the first four cumulants in terms of central moments.

A:

Q: Find the slope of the line through the point (12,15) that cuts off the least area from the first…

A:

Q: Determine the slope of the tangent line to the graph of ƒ (x) =- at the point(4, -4).

A: Use differentiation for finding the slope.

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Q: Show that cothx x+1 In X-1,

A: Solution

Q: Derive a formula for the absolute error of a quotient X2

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: