Q3:) The point moving on the curve y = x - 3x+5, such that ****, where (t) represents time. What is the rate of change of y, when t= 4? (10 Marks)

Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

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Q: 5. Find the slope of the tangent line to the curve y + 2yx3 - x-5y3 = 0 at (0, 5). %3D

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Q: Find slope of the tangent line to the elipse x^2/36 + y^2/16=1 at the point (x,y) slope=

A: Given ellipse equation is x236+y216=1 find the slope of the tangent line at the point (x,y)

Q: Estimate the instantaneous rate of change of y(t)=4t^2+5 at the point: t=−1 In other words, choose…

A: Given: y(t)=4t2+5. Now,          y'(t)=8t. At t = -1,           y'(-1)=8(-1)=-8.

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

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Q: ) Find an CIuation of the line tangent to the graph of Gec)=6e3X x tal dou2 o the Point (0,6). at

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Q: Find the slope of the tangent to the curve a+ 4xy+ y = 46 at (1,5). The slope is | (Enter undef if…

A: Topic = Derivative

Q: (b) y = x3 y 2 1

A: Given y=x³ Draw the graph and measure the change in y and change in x

Q: What is the slope of the tangent line to the curve xy +y– 1=0 at the point (0, 1)? -1 -3 -2 1

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Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

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Q: Estimate the slope of the tangent line at the point t= -2 for f(t) = 6t-3 (Give answer as a…

A: The given function is f(t)=6t-3 at t=-2

Q: For the function y = 8x2 + 6x + 2, at the point x = 5, find the following. (a) the slope of the…

A: Given function is: y=8x2+6x+2 and the given point is x=5

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

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Q: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

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Q: Find the equation of the tangent to the curve y= 2x? – 1 at the point where r = 1. Use limit…

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Q: Estimate the instantaneous rate of change of P(t) = 2t2 - 2 at the point: t = 3 In other words,…

A: Here we have to find the instantaneous rate of change of P(t)=2t2-2 at point: t = 3,

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). and to verify…

Q: Let f(x) = 6 - 3x + 5x2. (a) Find f'(a) (b) What is the instantaneous rate of change of f when x =…

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Q: 4) Estimate the instantaneous rate of change of function f(x) = x + 5x' +2 at x = -3 b) Determine…

A: Given that fx=x4+5x3+2First, we will find the instantaneous rate of change of the functionat x=-3.

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: If f(x) describes the position of an object over time, what is the average velocity on the interval…

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Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

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Q: For the functiony = 8x2 + 6x + 5,at the pointx = 8,find the following.(a) the slope of the tangent…

A: Given a function y = 8x2+6x+5.For any funtion f(x) the slope of the tangent at point x=a is…

Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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Q: Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.

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Q: (a) Find the equation of the tangent line to the curve y = 2lnx at x = 5.

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

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

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Q: Find the rate of change of the distance D between the origin and a moving point on the graph ofy…

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Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

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Q: The slope of the line through the distinct points (x1, yı) and (x2, Y2) can be interpreted as the…

A: To Determine: the slope of the line through the distinct points can be interpreted as the rate of…

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: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Given curve is y=x-1. Power rule of differentiation states that, ddxxn=nxn-1 Differentiating the…

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

Q: 8. What is the rate of change of the slope of the tangent line to the curve y =x – 3x2 +1 when x =…

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Q: What is the value of the slope of the tangent line to the curve *+4xy+y2=13 passing through the…

A: Note : As per guidelines, I have to answer Only one question, if you want other questions to be…

Q: Find the slope of the curve y^3+3x^2y-9y=-5 at the point (1,-1) and also find the rate of change…

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Q: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

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Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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Q: 2. At which points on the curve y = 1+ 60x – 2x does the tangent line have the largest slope?

A: Solution ) y = 1+60x3- 2x5 First derivative with respect to  x y' =0+ 60 ×3 × x2 - 2×5 x4 y' = 180x2…

Q: At what point on the curve x = 9t2 + 3, y = t3 – 2 does the tangent line have slope ? (x, y) =

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Q: A bug got into my graphing software and it is crawling around on a graph of y=x^4, in the first…

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Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

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Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00…

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Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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

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