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

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 the equation of the tangent line to the curve at a given point  y=x3-3x+1 (3, 19)

A: Given,

Q: For what value of x does the graph of y = eš (4x – 5)° have a horizontal tangent line? -

A:

Q: Show that an equation of the tangent line to the graph of =D2 at the point (a, b) is given by 2. b…

A: It is given that, Now take the derivative of the given function with respect to 'x'. Therefore,…

Q: Find the equation of the tangent line to the curve (y-2)² = 4x +5 at P(1,5).

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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Given curves x=2+lnt, y=t2+2 and the point 2,3. The objective is to find an equation of the tangent…

Q: Find the equation of the curve y = f(x) as shown in the figure with line tangent to curve at P(x ,…

A: The slope of the tangent at a point on a curve is equal to the derivative of the curve at that…

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…

A:

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: Write an equation for the tangent line to the graph of y = e* + x² + 1 at x = 0.

A: we have to write an equation for the tangent line to the graph of  at x=0.

Q: Find an equation of the tangent line to the graph of y = x^3 − 1 at the point where x = 2.

A: To find the equation of the tangent line at x=2.

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

A:

Q: b. b. y = 2 1+e-x at (0,1)

A:

Q: Find the slope, m, of the equation of the tangent line to the graph of y= (2x + 1)e* at the point…

A: derivative

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: Find the point on the curve y = x-11x+5 at which the tangent has the equati on y = x - 11.

A: We will find the  point on the curve at which the equation of tangent is given as following.

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: 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: Find y' and the slope of the tangent line to the graph of (3x- 2y)° = 2y2 - 9 at the point (1,2).

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Q: If y=mx+b is the equation of the tangent line to the graph of y = x - x- 3 and is parallel to the…

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Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

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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: If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k then what is the…

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Q: given x3   + y3 -9xy = 0,   find the point where the curve has a vertical tangent line

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Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…

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Q: Find an equation of the tangent line to the graph of y = e−x2 at the point 4, 1/e^16

A: Given curve

Q: Consider the following curve. Find y'(x). -*+4 y'(x) = (4 + *)? (+ )» Find an equation of the…

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Q: The curve y = [In (x + 4)]² has horizontal tangent line at the point(s)

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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: Find an equation of the tangent to the curve at the given point. x 3 , y = t2 3, (3, 4)

A: Given curve is

Q: Find an equation of the tangent line to the graph of y=e^-8x at the point (5,e^-40)

A: To find an equation of the tangent line to the graph of y=e-8x at the point (5,e-40).

Q: If y=mx+b is the equation of the tangent line to the graph of f(x) = X .2 - X at x= -1, then m= b3D

A: According to power rule of differentiation

Q: The equation of the tangent line to the graph of the function y = 7* – 4e² at a - O is

A:

Q: For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one…

A: Given curve is y=x3+kx2+3x-4. A curve have exactly one horizontal tangent  at x=a if f'a=0.…

Q: Find the equation of the tangent to the curve y = x + 5/x at point P(1,3).

A: Slope of Equation of tangent is dy/dx at point P.

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 for the tangent to the curve at y =x2 + 1, (4, 17) y = -4x - 15 O y = -8x - 15 y =…

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Q: Find the values of a and b for the curve x²y+ay²=b if the point (1,1) is on its graph and the…

A: It is given that, x2y+ay2=b   ...(1)and4x+3y=7    ...(2) Here equation 2 represent a tangent line…

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

A:

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: 3. Find y' and the equation of the tangent line to the graph of In(ay) = y²-1 at (1,1). 11: 11:

A: We have to find y' and equation of tangent

Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

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Q: Find an equation of the tangent line to the graph of y = e¯x- at the point ( 5, 25

A: given: y=e-x2; 5,1e25 we know that for finding equation of tangent at point5,1e25, we need to find…