Show that the graph of the inverse of ƒ(x) = mx + b, where m and b are constants and m ≠ 0, is a line with slope 1/m and y-intercept -b/m.

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 the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: Differentiate implicity to find the slope of the following curve at (0,3) x^3+yx^2+x^2-3y^2=0

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Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find  the slope of the secant line between x=2 and x=5 on the graph of the function…

Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

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: Given the function f(x)=x^3+9x^2+19x+4, determine all coordinate points (x,y) on the graph of f such…

A: Differentiate the given function and equate to -5 and find coordinate points.

Q: If ƒ′(x) = 3x + 2, find the slope of the line tangent to the curvey = ƒ(x) at x = 1, 2, and 3.

A: Slope of the tangent line is the derivative of the given function at the given point. Therefore…

Q: Find an equation of the line that is tangent to the graph of the function f(x)= 2x and parallel to…

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Q: Suppose the slope of the curve y = f'(x) at (4, 7) is §. Find f'(7).

A: Given slope of the curve y=f-1(x) at (4,7) is 45

Q: Find an equation of the line tangent to the graph of f(x) = at 8,

A: f(x)=4x

Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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Q: Find the slope of the secant line connecting the points on the graph f(x)=2h+4x-12, with the given…

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Q: Suppose that f is a linear function with slope -3.2 and that f (3) = 6. What value of x gives f(x) =…

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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: 1) What is the slope of the graph y = 5e³x at x = 1?

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Q: Find the slope of the tngent line to the graph of the given function at the given Value of X.…

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Q: Suppose that f is a linear function with slope -3.6 and that f (2) = 8. What value of x gives f(x) =…

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Q: The slope of the curve f(x)= at x =1 is

A: given function :

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 equation of the line tangent to the graph of the function at the indicated point…

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Q: The gradient of the line with equation y = 2x – 3 is: 3 O 2 O 3 O -3

A: Here, the given equation of a line is: y=2x-3

Q: Determine the equation of the vertical trace of the function g(x,y)=-x^2-y^2+2x+4y-1 corresponding…

A: To find equation of vertical trace we need to substitute value of variable in the given equation of…

Q: Find the equation of the line tangent to the graph of the function at the indicated point. 20) f(x)…

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Q: Find the deritative of f(x)= 5/x^4 + -7/x^3 - 3/x^2 Then calculate the slope of tangegent at x=-1

A: We find the deritative of f(x)= 5/x^4 + -7/x^3 - 3/x^2   Then calculate the slope of tangegent at…

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: ATTACHED THANKYOU

A: Given that the first term of the AP is a and common difference is d.And the AP is constructed by the…

Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

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Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−3x3+4x2+2.

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Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: If the slope of an arbitrary curve y=f(x) at a point p0(x0, f(xo)) is S. So do you think the slope…

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Q: Find the slope of the curve f(x)= x2 at the point P(2,4)

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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 the equation of the line tangent to the graph of f(x) = ₂ at x = 3.

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Q: At what point on the graph of f ( x ) = 2x 3 - 3x 2 - 8x is the slope of the tangent line equal to…

A: The function is f(x)=2x3-3x2-8x and the slope of the tangent line is given as 4. By definition, the…

Q: Suppose that f is a linear function with slope 4 and that f(2) = 7. Find the equation for f with…

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Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: Find the slope of the line tangent to the graph of the function at the given value of x. 5/2 y = 9x…

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Q: Find the slope of the line tangent to the graph of the function at the given value of x. y = x4 + 2x…

A: Given : y = x4+2x3+2x-2

Q: At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations…

A: a) Points are (1,-2) and (-1,2) b) Lines are y=-x-1, and y=-x+3

Q: At what points on the graph of ƒ(x) = x3 + 6x2 + 21x + 2 is the slope of the tangent line 9?

A: Given:  f(x)=x3+6x2+21x+2Slope of tangent line=9 To Find: Points where the slope of tangent line is…

Q: . Given the relation x2 – xy + y3 = 11, determine the slope of the line tangent to the curve at…

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Q: find the slope of the line tangent tothe graph of ƒ(x) = 5 at P(1, 5).

A: We know the slope of the tangent line to the curve y = f(x) is dy/dx.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.