Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs using a calculator or computer that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Enter your answers as a comma-separated list. Round your answers to three decimal places. If an answer does not exist, enter DNE.) (2x + 3)?(x – 2)5 x³(x - 5)2 f(x) =

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: Consider the funchionE foc) =-X+4x-2. a) SKetch the of f in the interval graph [-1,5]. b) Find…

A: Given a function f(x)=-x2+4x-2 Let y=f(x), To sketch the graph of f in the interval [-1,5] and to…

Q: Use implicit differentiation to find the point in the first quadrant on the ellipse 8x2 + 4y? slope…

A: Question- Use implicit differentiation to find the point in the first quadrant on the ellipse 8x² +…

Q: Given y=xx+4). Plot any stationary points, inflections points, and cusps which may or may not exist.…

A: Given, y=x23x+4 Used formulas, ddxxn=nxn-1ddxconstant=0Product rule of…

Q: The curve f(x) = 27/(x^2+9) is called the Witches of Agnessi. Find the equation  of the tangent line…

A: Given- fx=27x2+9 To find- The equation of the line that iis tangent to above curve at the point…

Q: Find the equation for the tangent to the curve at the given point.

A: First find slope using y'Slope=48

Q: 5x The graph 1 has a horizontal tangent at a =

A: Topic -point of horizontal tangent To cuve point of horizontal tangent To graph is at x=6/5

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3.…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = = y = 1 4(x - 5),…

A: The given equation is; (y-3)2=4(x-5), (6,5).

Q: Find the horizontal and vertical asymptotes of the curve. y = 7ex ex 4 - X = y = (smaller y-value) y…

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Q: Find an equation of the tangent line to the parabola at the given point. y 15 10 x² = 8 y (7, 49/8)…

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Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: 2. Consider the function h(x) = 11 - + x3 a) Find the equation of the tangent line to the graph of h…

A: We will find the equation of tangent line as shown below

Q: If f(x) = 2x- 7x + 5, find f'(- 1). 2x- 7x +5 at the point Use this to find the equation of the…

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Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

Q: 1. Where does the graph of s= t² - 3t+2 have horizontal tangent? Write an equation for the tangent…

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: The graph of 3 (x+y) = 25 (x -y²), shown in the figure, is a lemniscate of Bernoulli. Find the…

A: Given query is to find equation ifbthe tangent at given point.

Q: (a) If F(x) = 12x/(3 + x2), find F '(3) and use it to find an equation of the tangent line to the…

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Q: c) Finally, draw a large and clear sketch of the graph of f(x) = 2² – 2 and illustrate the tangent…

A: The point slope form y-f(x0)=f'(x0)(x-x0) is the standard equation for tangent line, where (x0,y0)…

Q: 50 Find the length of the curve whose equation is given by r = e on 0 < 0 < 2T.

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Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 6 if g(6) = −2 and g'(6) = 5.…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -4 andg' (6) = 3.…

A: Slope intercept form-  Y = mx + c  m = slope = g'(x) At x=6,  m= g'(6) =3 c= intercept on y axis…

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=n

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Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

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Q: Find the slope mm of the tangent line to the parabola f(x)=x^2+7 the point (5, 60) by using the…

A: topic - equation of a tangent line

Q: If f(x) = 5x2 - 4x, find f'(2) and use it to find an equation of the tangent line to the parabola y…

A: Given that fx=5x2-4xTo find : equation of tangent at point 2,12 and f'2Solution…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -2 and g'(4) = 3.…

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Q: Find the equation of the tangent line to the graph of y =f(x) at the point where x=-3 if f(-3) = 2…

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Q: 6x Find an equation of the tangent line to the graph of y = 2 X +1 at the origin and at the point…

A: Given,          The line is y=6xx2+1 at the origin and at the point -1,-3.To find : Find an equation…

Q: 2x - T find the equation Given the tangent funchions of y- 1-3+tan (") Of all its vertical…

A: y=1-3tan2x-π4 Now it can be written as, ⇒y=1-3·sin2x-π4cos2x-π4⇒y=cos2x-π4-3sin2x-π4cos2x-π4

Q: Find h'(-3) if h = f o g, f(x) = -8x? + 6 and the equation of the tangent line of g at -3 is y = 7x…

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Q: If f(x) = 2x - 2a + 6, find f'(– 1). 2x - 2x + 6 at the point (-1, Use this to find the equation of…

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Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=7

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Q: Find all values of x at which the tangentline to the curve y = 2x+13 has the y-intercept 2. x+6…

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Q: An equation of the line tangent to the graph of g at x = 3 isy = 5x + 4. Find g(3) and g′(3).

A: The tangent line of function g at x=a is defined as y-ga=g'ax-a

Q: Q 8/ Find all points on the graph of f(x)= (x-3)(x-2) at which the -1 tangent line is horizontal.…

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: Consider the graph of f(x) = 11-x^2. Find the coordinates of the point P in the graph at which the…

A: Let the tangent passes through (h,k) (h,k) is on f(x) = 11-x2. So k=11-h2 That means (h,k)=(h,…

Q: Given the cosecant functions of y=csc(x/2-π/2) find the equation of all of its vertical asymptote

A: We know that the Cosecant function only has vertical asymptotes. It does not have any horizontal…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -8 and g'(4) = 71.…

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Q: For what value(s) of x does the graph of 1 f(x) = – x² +3 have a .2 - horizontal tangent?

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Q: For the curve f(x) = 1+40x^3-3x^5 , what is the point of inflection (maximum) of the tanent line…

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Q: The graph of y = fx) and the tangent to the curve at x = 1 is shown below. ..... 5 3 y - f(x) -1 0.

A: Consider the given figure.

Q: 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 %3D = - 3x2 f(x) = 4…

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Q: At which point(s) does the graph of  y= e((x3-2x2+3x)/(x)) have a horizontal tangent line?

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 3.…

A: The tangent line is a Straight line which is a tangent to the curve at the point. The point here…

Q: 8x at the point (1,4). x +1 Find an equation for the tangent to the curve y =

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Consider the given function as y=5x1+x2