Two small arches have the shape of parabolas. The first is the graph of f(x) = 1 – x² for –1 < x < 1 and the second is the graph of g(x) = 4– (x – 4)² for 2

Q: If the slope of the tangent line to the graph of y%3f(x) at x-Da is m(a)%=D2a+1, and f(1)=5, then…

A: Given: If the slope of the tangent line to the graph of y=fx at x=a is ma=2a+1and f1=5. To Find: f2…

Q: Find a cubic function y = ax + bx2 + cx + d whose graph has horizontal tangents at the points (-2,…

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1).

A:

Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

A: We find dy/dx at x=1 and y=2  So the slope of the tangent = 9/4

Q: If the slope of the tangent line to the graph of y=f(x) at x=a is m(a)=2a+1, and fl-1)=2, then what…

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Q: 1 The slope of the tangent line to the graph of y = at a = 1, is 3e². %3D e (r + 2) Select one: a.…

A: Given curve: Now,

Q: Find the slopes of the tangent lines to the graph of f(x) = 2e² at the points (0, 2) and (1, 2e).

A: See the attached file to know how to find thesthe of a tangent at the given points.

Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

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Q: Find the equation(s) of the tangent line(s)to the graph of the parabola y = x2 through the given…

A: Given, y=x2

Q: - Does the graph of fo, x< 0 1. r20 U(x) = have a vertical tangent line at the point (0, 1)? Give…

A: Given: The function To check: Whether the given graph has vertical tangent line at the point (0, 1)…

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: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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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: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

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

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Q: What is the slope of the tangent to the curve y=arctan 4x at x= 1/4 A. -2 B. 0 C. 1/2 D. 2…

A: To find the slope of tangent to the given curve.

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: The graph of ax + b f(x) = (x+ 1)² has a horizontal tangent line at (-2, –1). Find a and b.

A: Given,           The graph of fx=ax+bx+12 has a horizontal tangent line at -2,-1.

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

A:

Q: Find a &gt; 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

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: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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Q: Show that the equation of the tangent ine to 'the graph of the parabola at the point Pt'=(t,t²) 1s…

A: Consider the given function whose equation of tangent is required to calculate.

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: Find the slope of the tangent line to the graph r=2sin(0) at the point V3, 3 11.

A: We have to find

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Find the slope of the tangent line to the graph at the given point.

A: Given: x3+y3-6xy=0,     43,83

Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

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Q: y = 3x?+1 ; (0,1)

A: Solution ) slope of the tangent line by the limit definition = m = (dy/dx) [ x = 0 becuase we have (…

Q: If y-mx+B is thế équation of the tangent line to the curve X +2xy – y+ x = 39 at x=5 with a negative…

A: At x=5 we find y The points are (5, 1) and (5, 9)

Q: 2. Consider the graph of g(x)-2+3-1 a Lt anyalues at which g)net dafferentiable Setch the tangent…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

Q: Find an equation of the tangent line to the parabola y=x2  at the point P(1,1)

A: To find an equation of the tangent line to the parabola y=x2 at the point P1,1

Q: Find an equation of the tangent line to the graph of y = g(x) at x = –1 if g(-1) = 5 and g' (-1) =…

A: Concept: The Equation of tangent to the graph y = g(x) at point (x1,y1) is given by: (y -y1) =…

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: 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: Find all the points of the graph of y = (x - 2)2 at which the tangent line is perpendicular to the…

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Q: - Find the value of 'a' for which the tangent to the curve f(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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Q: 45. What is the maximum slope for the curve y= In(x +9)? %3D O A A 3 OB In 9 OC 3 OD There is no…

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Q: Let f(9)=−4 and f′(9)=−4. Then the equation of the tangent line to the graph of y=f(x) at x=9 is:…

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Q: i. Find the equation of the tangent to the graph of g at (4, 2).

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Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: Find an equation for the tangent line to the parabola y x*at the point P(1, 1). %3D

A: Given,            The parabola is y=x2 and the point is P1,1.We know that,            The equation…

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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