Let P(x, y) be a point on the graph of y =√x. Express the distance, d, from P to (1, 0) as a function of the point’s x-coordinate.

Q: For the function y = (x − 2) In x, what are the two x intercepts, and between the two intercepts, is…

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Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D

A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

Q: f(x) = −x2 + 6x − 12 y-intercept(x, y)=

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 4 – 3 x, and the line…

A: Given: f(x)=4-13x If the given line is y=mx+c with slope m then the slope of a line perpendicular to…

Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 – -x, and the line…

A: Given data:     The expression of the first equation of the line is: f(x)=5-2x/3. The second…

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Q: Let f (x) = Vx. %3D Find the slopem and the point-slope equation of the line tangent to the graph of…

A: If a function gx represents a curve then g'a represents the slope of curve at x=a.

Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: Consider the point (x,y) lying on the graph of the line 2x+4y=5 let L be the distance from the point…

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Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x, y) = xey –…

A: To find the direction in which the function is increasing most rapidly.

Q: Find the linear approximation of the function f(x) = Vx+3 at a = 1 and use it to approximate the…

A: Given the function fx=x+3. Find the linear approximation of f(x) at a=1 and use it to approximate…

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Find the coordinates of the point(s) at which the line tangent to the graph of the function f (z)…

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Q: Find the X coordinates to the curve Y= X^5 - 5X^4 when the gradient = 0

A: Given equation is Y= x5- 5x4 Gradient =0

Q: Find the extremum points of the function f(x,y) = y² +x*y +x² - 2y and determine the nature of the…

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Q: Use the EVT to find the maximum and minimum values of the function f(x, y) = e4a-5 yʻ on the disc x²…

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Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

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A: We have to find the level curves .

Q: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

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Q: f(x) = x², with 0 < x < 6

A: Length of the curve y=f(x)  from   x=a to x=b   is give by  L=∫ab1+dydx2 dx

Q: 1- at 9=0

A:

Q: Given that f(−2)=−8f(−2)=−8 and f′(−2)=−7f′(−2)=−7, find an equation for the tangent line to the…

A: Given : f(-2) = -8, f'(-2) = -7   To find the equation of the tangent line to the graph of y= f(x)…

Q: Pls help on this question. ASAP

A: Given the function f(x) = -x2 + 5 We need to find slope of the secant of f(x) between x= -2 and x =…

Q: The level curves of the function f (x, y) = V2x2 + y? – 1 are

A: Please refer to the image below

Q: Find the direction in which the function is increasing most rapidly at the point P 0. f(x, y) = xy 2…

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−1/3x, and the line perpendicular…

A: We have to find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line…

Q: Show that, for any cubic function of the form y = ax + bx² + cx + d, %3D there is a single point of…

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Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

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Q: Find the analytic function whose imaginary part is v =2xy

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Q: 4. Find all the points at which the direction of fastest increment of the function f(x, y) = x² + y²…

A: According to question,Given Function,fx, y = x2 + y2 -2x -2y

Q: Determine the stationary values of the function z = x3 – 6x² – 8y² and distinguish between them

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Q: For the function f(x,y.z) = 3 + 4xy - 5z*, find f,, f, and f,.

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Q: Differentiate the function. y = In(12 + t – t31)

A: We have to find derivative

Q: Consider the point (x, y) lying on the graph of the line 2x + 4y = 5. Let L be the distance from the…

A: Given,

Q: f(x) = + 3, X with 0 < x< 3

A: The length(arc-length) of the function is given by: L=∫ab1+(f'(x))2dx

Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: Produce the linear approximation of the given function at the specified value. f(x) = sqrt(x); x =…

A: fx=x,  x=2 Differentiating with respect to x, we get f'x=12x Now at x=2, f2=2  &amp;  f'2=122

Q: Consider the function f(x, y) = x² + xy - 5x- y+1. Then:

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Q: 3 f(x) = x2, with 0 < x < 1

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Q: f(x) = + 2x' with 1 < x< 2

A: Given: fx=x36+12x with 1≤x≤2

Q: Consider the point (x,y) on the graph of the line 6x+4y=7. Let L be the distance from the point…

A:

Q: Find k so that the function f(x) = x² + kx will be tangent to the line y = 2x-9

A: Here, the given function is: f(x)=y=x2+kx...(1) And also given that the tangent line to the given…

Q: Find the linearization of the function at a . f(x) = sqrt  x    , a = 4

A: Consider the provided function, fx=x,    a=4 Find the linearization of the function at a. Apply the…

Q: f(x) = 2x2 + 10, g(x) = 4x + 16

A: Sketch the curve f(x) and g(x) in same phase

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

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Q: (b) Use the result of part (a) to find the direction in which the function f(x, y) = x³y - x²y4…

A: Given:

Q: Find the domain of the function flx, yl= %3D

A: Explanation is given below...

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: