3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

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 the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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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: Differentiate implicitly to find the slope of the curve at the given point. xy3-x5y2=-4; (-1,2)

A: Given:- xy3 -x5 y2 =-4  To find:- slope of tangent at point (-1, 2)

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

A:

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

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Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

A:

Q: Determine the equation of the line tangent to the graph of y = x° + 2x at the point (1, 3).

A: y=x3+2x   x1,y1 =1,3dydx=3x2+2slope of tangent at point1,3dydx1,3=312+2 = 5Slope of the tangent m =…

Q: What is the gradient of Y = x³ - 3x² + 4, when x = 1?

A: Gradient is the rate of fastest decrease at a particular point. In other words it is the derivative…

Q: what is the gradient of y=x3-3x2 +5 when x=1

A: Given y=x3-3x2 +5

Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x=axis ?

A:

Q: (iii) On your graph, draw a tangent to the curve, y = 2x +-10, that has a gradient of 1.

A: Given curve is y=2x+16x-10 Now, find the first derivative. y'=2-16x2-0y'=2-16x2 If the gradient is…

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

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 slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

Q: FInd the equation of a linw whose gradient is 3/2 and which passes through the point P,where P…

A:

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: what is the gradient of 3x + 2y + 14 = 0

A:

Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

A:

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: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: Determine slope of a curve y = x³3 + 1 at x = 1

A:

Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

A:

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: Find the eqaution of the curve that passes through (0,1) if its slope is given by y'=1/2X at any…

A:

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

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 slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

A:

Q: The gradient at (-2,1) is

A:

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.…

A:

Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find the gradient of the curve . Y=4x^2 at x=3

A:

Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

A:

Q: The equation of the line with gradient 4 which passes through the point (1,2) is: O y = 2x – 4 y =…

A: Equation of line can be taken as y=mx+c

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

A:

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A: