The equation of a curve is y =x'+ax + bx, where a and b are constants. (1) In the case where the curve has no stationary point, show that a < 3h. (I) In the case where a =-6 and b=9, find the set of values of x for which y is a decreasing function of x.

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The…

A:

Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

A:

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A:

Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

A:

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

A:

Q: 1) Find the slope of the tangent lines on the curve y = 6x + 24x -39x - 43 at points | (-5,2) and…

A: Slope of line is given by m = dy/dx = tan θ y = 6x3 + 24x2 - 39x - 43  Differentiating with respect…

Q: Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x,…

A:

Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

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Q: equation of the curve that passes through the point (0, 6) and whose slope at (x, y) is x/y.

A:

Q: Find an equation for the tangent line to the curve y = xV 2x² - 14 at the point (3,6). O y- 6 = 14(x…

A: The equation of the tangent line to the curve is, y - 6 = 11(x - 3)  The detailed solution is as…

Q: _1. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? a. -5 b. -6…

A: Using Derivatives &amp; Application of derivatives

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: 8. Find the slope of the tangent of the curve x² + y² = 10 at the point (1, -3).

A:

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

A:

Q: Find the slope of the curve y=x^3-3 at the point ​P(-2,-11​) by finding the limiting value of the…

A: Given,y=x3-3Point P -2,-11The slope of the secant line ism=fb-fab-a

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0

A: Clear solution is given.

Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

Q: Find the equation of tangent line to the curve y = 2 - x 2 (7, ²/7). at the point (7, Express the…

A: The objective is to find the equation of tangent line.

Q: . Find the gradient of the TANGENT LINE at the given points y = 4 - 3x2         at (-1, 1) y = x2 -…

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Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

A:

Q: 2. Find the equation of the tangent line to the curve y = x³+ 2x² – x at the point (-2, 7).

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

A:

Q: 4. The slope of the tangent line to the curve y 4. is: 9 - at the point 9, The equation of this…

A: To find the slope of the tangent line to the curve, y=4x, at the point 9, 49.The  equation of this…

Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С.…

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: 11. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? %3D a. -5 b. -6…

A:

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

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Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: What is the equation of the curve that passes through the point (0, 3) and has a slope at any point…

A: We have to find

Q: Find the equations of all tangent lines to the curve x2 + 4y² = 8 that pass through the point…

A: Given curvex2+4y2=8Differentiate above curve w.r.t…

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x - 4 and parallel to the line 6x…

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Q: A heat-seeking particle is located at the point (2,3) on a flat metal plate whose temperature at a…

A:

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: Find the equation of a Tangent line to y = 2x2 – 5x – 1 that is parallel to line x + y –

A:

Q: 3 - at the point (3, 1) is: The slope of the tangent line to the curve y The equation of this…

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

A:

Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: Find the equation of the tangent line to the function f(x) = 8/x - 2 at the point (64, 62). Provide…

A: To determine the equation of the tangent in the form y =mx+b

Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

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: