Show that the graph of y = 5 and y = log,. x are reflections of each other with respect to the line y = x.

Q: Find the equation of the tangent line at the given point on each curve. :x2 + y2 = 100; (8, -6)

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Q: 2x+1 S(x) = 3x+2,

A: Solution:Given     f(x)=2x+13x+23To find the derivativeFormula:ddx(xn)=nxn-1uv'=vu'-uv'v2

Q: The slope of the tangent line to the graph of the function y = 7V-3 at (9, 18) is

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Q: Find an equation of the tangent line to the graph at the given point. x^2y^2-9x^2-4y^2=0, 4,2sqrt3

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Q: Show that the x-coordinate of the vertex of the parabola whose equation is y = ax2 + bx + c occurs…

A: Given the equation of a parabola y=ax2+bx+c

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: sketch the shifted exponential curves y = 3x + 2 and y = 3-x + 2

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

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: Find the equation of the secant line on the curve f(x) = -x²+2 passing through the points xo = -1…

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: y = (e* + 1)*

A: We have, y=ex+1x On taking logarithm on the both of the side, we get the result as logy=xlogex+1…

Q: Find an equation of the tangent line to the graph of the function at the point (9, 1). y = 2x - 9

A: Concept - used the formula of y-y1 =m(x-x1)  Here m=dy/dx=slope

Q: Is there a relationship between X and Y?

A: If the variables in the study are measured on ordinal scale, then researchers employ Spearman's rho…

Q: IF THE CURVE OF THE FUNCTION F (X) = Y PASSES THROUGH THE TWO POINTS (2,2) AND (1, K) AND SATISFIES…

A: We have to solve given problem:

Q: The slope of the tangent line to the graph of the function (16, 24) is - O 1.25 O 0.88 O -2.00 | O…

A: Given function -  f(X) = y = 7√x -4

Q: Find the dy/dx of the following function using Chain Rule. y=(-5x3 - 3)3

A: Find the dy/dx of the following function using Chain Rule.

Q: sketch the shifted exponential curves y = 1 - ex and y = 1 - e-x

A: Given  The parent exponential function y=1-ex . To find the graph of the exponential function…

Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: What is the decreasing and what is the constant

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Q: Find a function of the form y = Asin(kz) + C or y = A cos(kz) + C whose graph matches this one: -8…

A: The maximum point on the graph is at 3  . that is y intercept is at (0,3) When the maximum point is…

Q: Suppose C is the graph of y = f(x) for a < x < b. Compute x dy + y dx in terms of f.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the derivative to find the vertex of each parabola y = ax2 + bx + c

A: Given the function y = ax2 + bx + c We need  to use the derivative to find the vertex of  parabola.

Q: Find the function f whose graph has slope 2x2 + 4 df dx and which passes through the point (1, 1).

A: Given: The slope of the function is, dfdx=2x2+4x

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: Determine the point(s) (if any) at whi

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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 an equation of the line tangent to the graph off(x) at the point (5, 9):f(x) =e^(x^2−3x−10)+ 8

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Q: Select all the lines that are needed to find the inverse of y = log, (x + 1) – 2 in the appropriate…

A: Given,y=log3(x+1)-2

Q: Determine the equation of the tangent to the graph of y- x - 3x + x+3 at the point (- 1, -2). O a)…

A: We have to find the tangent of the given function at point (-1,-2).

Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

A: Given first derivative is:

Q: Show that the graph of y = 3* and y = log,x are reflections of each other with respect to the line y…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: find an equation for the tangent line to the graph of y=(5-2x)^2 at (3,1).

A: Explanation of the answer is as follows

Q: Find an equation for the line tangent to the graph of f(x)=-5xe^x at the point (a,f(a)) for a=3…

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Q: Find , where y is defined as a function of x implicitly by the equation below. dz' 2y5 - 2ry = -2…

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Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.

A: The given function is,

Q: Graph the Ine whose x-tercept is -I and whose y-intercnpt is 1.

A: Given,           The line whose x-intercept is -1 and y-intercept is 1.We know that,           The…

Q: Suppose that the graph of x = f(y) lies to the left of the y-axis. Is f(y) dy positive or negative?

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Q: Find the equation of the curve that passes through the point (3, 8) if its slope is given by dy 3x –…

A: We have to find equation of curve

Q: Suppose that z is inversely proportional to y, and that z = 12 when y =16. Write an equation that…

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Q: Two vehicles start out traveling side by side along a straight road. T owing graph, are given by s =…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If the function y =2= is reflected in the line y =z, the equation of the transformed image is Oy =…

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Q: Find the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function:

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

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Q: Sketch the graph of h(t) = |t| + |t + 1|

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Q: Find an equation of the line tangent to the graph of f(x) = · 1 (2) a) at (1,1); b) at - 3, 27 c) at…

A: To find an equation of the line tangent to the graph: