1. Find a function y = f(x) having at least three inflection points and sketch its graph. [Note: To find the formula of f(x) start with a suitably chosen f"(r) and integrate f"(x) twice. The second part of the question is a curve sketching problem. Give all details. ]

Q: (1 )  (a)  Find two positive numbers x and y whose product is maximum and 2x+y=100. ( b )  Find…

A: a. Given The product is given by P=xy Plugging the values: For P to be maximum, the derivative…

Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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Q: Differentiate

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: 글 -x Equation of the tangent to the curve y =e +1 at x =0 is O 2x+y=4 O x+2y=4 O. x-2y=4 O 2x-y=4

A: Given curve is y=e−x2+1 and x=0. We have to find the equation of tangent to the curve y=e−x2+1 at…

Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

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Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: 11.Determine the equation of the curve whose tangent line at any point (xy) is e* – sin x and passes…

A: Given problem:- Determine the equation of the curve whose tangent line at any point (x,y) is ex -sin…

Q: -2x²+2x+1 Find the equation of the tangent line to the graph of F(x) ev dy at x = 0. sech z

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Q: 23. Find all points of inflection of the curve y=2r – 12r² + 10x+3. A) x=-1 and x= 1 B) x=-1 C) x=-1…

A: As per our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: 3. (a). For a curve defined by an equation f(x), satisfy dy + (1 – 2x)y = 4x for x > 0 and - dx f(1)…

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Q: 17. The equation of the tangent line to the curve y = at the point (3, ÷) is 2 A. x+16y+11= 0 B.…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

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Q: 5. Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given parametric equations are, x=t3+cosπt, y=4t+sin2t+6. Find the equation of the tangent to…

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations…

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Q: 2. Find the equation of the line tangent to the curve at the point indicated. Express your answer in…

A: As we know that; The slope of the tangent line to the curve at a given point Px0,y0 is equal to the…

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

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Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x…

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Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: The graph of the function y = 3 sinh 4x has a relative maximum at a point O (0.0) O (0, 3) O (3.0)…

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Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: 6. Find all values of x in the interval [0, 2 n] for which the slope of the tangent to y e* csc(x)…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: 1. Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for x > 0 (a) Calculate f'(0),…

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Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

A:

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: 1, Differentiate the function. (1) f(x)= /32 (2) f(x)= (x°+10) 5 (3) f(x)= 2.x - V х (4) f(x)=…

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Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: 1. Find an equation of the tangent to the curve, x = t + 1, y = t4 + t corresponding to t = - 1.

A: To find the equation of tangent for following curve x = t3 +1    .... 1 y = t4 + t    ..... 2 AT t =…

Q: Consider the step size h = 0.1 and h = 0.001, how does the step size affect the accuracy in %3D…

A: Given that, A=82, B=16.4f(x)=Aex+Bx2sinxFor the given values of A and B,f(x)=82ex+16.4x2sinxWe need…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 11.Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and…

A:

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: 11. Find an equation of the tangent to the curve y = In(4 + x") at the point %3D 12. i) Find the…

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Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

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

A: Using formula of equation of tangent line.