Given that a line with gradient - is a tangent to C, and touches C at the point T. (d) Find an equation of the line which passes through A and T.

Q: Suppose you are standing in a field near a straight section of railroad tracks just as the…

A: As a first step, let's convert the given information in a diagram. Please see the white board.Let A…

Q: 3. Determine the value of b if the slope of the tangent to f(x) = (3x² + 1)(2x² + b) at x =– 1 is –…

A: given,       fx=y=3x2+12x2+b    slope of the tangent, at x=-1      dydx=-16

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

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Q: y = −2x4 + 4ax³ - 5x² - 8x + 1

A: Solution:-

Q: Given f (8)-3, f'(8)--5, find the equation of the tangent line at x - 8 a) y+3 (x-8) b) Oy +5 -3(r -…

A: We have been given f(8) = 3 and f'(8) = -5 and we need to find the equation of tangent line x=8.

Q: What is the slope of the tangent line that touches the graph of In y +es-1 = 3y – 4z at the point…

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Q: Determine an equation of the line tangent to the curve at the given point. 4x² + 4xy + 3y 51, (3,1)

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Q: Find the equation of the line which is tangent to the granh of y .3r2 2r + 4 at tho

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Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: What is the slope of the tangent line of y = 3x- 2x2 + 2x -5 at x = 0? A. 2 B. -5 C. D.

A: Given equation of the curve is y=3x3-2x2+2x-5   x=0 find slope of the tangent

Q: What is the slope of the tangent line that touches the graph of In(y) + e2* -'=3y – 4x at the point…

A: Given that:  lny + e2x-1 = 3y-4x We find slope of the tangent line at point (1/2,1) . Here i…

Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

A: I have stated the used method in the brackets

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,          x=t2-4 , y=t3+6t , t=3To find: The equation of the tangent line.We know that,…

Q: What is the equation of the Tangent Line to the curve y = 3 x – 4 x 2 at (-2, – 22)7 A 19 x + y = 60…

A: Topic = Application of Derivative  Correct answer = C

Q: find the equation of the line tangent to the curve at the given point x2y2=4y ;(2,1)

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Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

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: tangent to the curve x^3 +x^2 y + 4y - 1 + 0 at the point (3,-2) has a slope equal to: a. -13/15…

A: We will find the slope.

Q: Which is the equation of the tangent line to the curve x +xy = 4+ y² at the point (4,6)? a) y-6=3(x-…

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Q: 4. At what point on the graph of y = ÷x² is the tangent line parallel to the line 2x – 4y = 3? A.…

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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: Find the equation of a line tangent to the curve xy = (√xy -x) + 1 at the point (1, 2). A. y= 2-x…

A: Here given equation as Differentiate with respect to x

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

Q: Use your answer from the last problem to find the slope of the line tangent to f (x) = Vx at x = 9.

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Q: Find the equation of the tangent line to the graph of the function f(x) = 4x - at x = -2. Give your…

A: Use formula of equation of tangent line.

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: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

Q: find equation for the lines that are tangent andnormal to the curve at the given point.x^3/2 +…

A: Given: x32+2y32=17    at the point (1,4)

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Given the curve y= x^3 - 4x +1 . Find the equation of the tangent at the points where the slope of…

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Q: B) Find the equations of all lines having slope-1 that are tangent to the curve y = -3)

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Q: c. Find the equations of the line tangent to the curve y = x³ + x, where the slope is equal to 4.

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Q: Show At what points does the equation of the line tangent to the curve y=1/x+3 have a slope equal to…

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Q: The slope of the tangent line to the curve C at the point (1, 2) is A) 4 B c) 2 D - 4 2.

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Q: determine the constants a and b so that the line y = -3x + 4 is tangent to the graph y = ax^3 + bx…

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Q: If f'(4)= 6 and g'(4)=3, then the slope of the tangent line to the graph of y=2f(x)-5g(x) at x=4 is…

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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: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

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Q: What is the slope of the tangent line to the graph of y = x3 – 4x + 2 at point (2, 2)? %3D А. 1 В. 4…

A: Given function, y=x3-4x+2Diferentiate w.r.t.…

Q: What is the slope of the tangent line that touches the graph of In y + e2¤¬1 = 3y – 4x at the point…

A: Given query is to find the slope of the tangent.

Q: At the two points where the curve x2 - xy + y2 = 36 crosses the x-axis, the tangents to the curve…

A: x2-xy+y2=36

Q: Find y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: If f(x) = 2x2 - ax - a, b, c ER, then a +b – c=? 4 and the equation of the tangent line to the curve…

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Q: What is the slope of the tangent line that touches the graph of In(y) +e2-1=3y – 4x at the point 3 A…

A: We have to choose the correct answer from the given information according to the given information

Q: Let a, b, and c be constants. Find the equation of the line tangent to f(x) = (x − a)(x − b)(x − c)…

A: The given function is: f(x)=(x-a)(x-b)(x-c)

Q: The equation of the tangent line to the curve a? +y = 25, at (8,-12) is. 12 (x+8) – 12 8 y = 8. y =…

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Q: 3. Determine the value of b if the slope of the tangent to f (x) = (3x² + 1)(2x² + b) at x = – 1 is…

A: The formula to find the slope of the tangent to the function f(x) is f'(x).

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.