Consider the function f(x) = 5x + 9. Its tangent line at x = 3 goes through the points (7, yı) and (-9, y2) where %3D y1 = , and y2 =

Q: Find the equation of the tangent and normal line of the function f(x) = 2x – 1 at the point (5, 3).

A: fx=2x-1   First find equation of tangent line of given function  We need to find the slope of…

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: Find the gradient of the tangent line to y when x = 2.

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Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: Find an equation of the tangent line to y = xt + 2x2 – x at x = 2

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Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: z = Vx4 + yf, fz (1, 2)

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Q: 5. Find the equation of the tangent line on x² + y? = (2x² + 2y² – x)² at (0, ).

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Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Find the point on the curve y=x√x for which the tangent line to the curve is perpendicular to the…

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Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Pls help ASAP

A: This question is related to equation of straight line, we will use differentiation to find the…

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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Q: Find the equation of the tangent line to y = arctan(2x) when x = V3 O y - = ( - ) 1 3 O y - = }(2 -…

A: Let's find.

Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: Determine the equation of the tangent line to the function y = 2 + xe³x + x when x is equal to 0.

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find the point of intersection of the tangent line to y=sin 2x) at y=0 and the line x+2y=5-

A: Given: y=sin(2x)  and y=0       substituting y=0 in y=sin(2x)then    0=sin(2x)         2x=0…

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: Determine the equation of the line tangent to x² + sin y = xy² +1 at the point (1,0).

A: The equation x2+siny=xy2+1, we have to determine the line of the tangent at the point (1,0).

Q: Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

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Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find an equation of the line tangent to y = xsin x at the point x = 1.

A: The given equation is y=xsinx.

Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

Q: Estimate the indicated derivative by any method. x = 4t + t2; estimate ds/dt | t= -2

A: Given, x=4t+t2 We have to find dxdt at t=-2 We will use following formula to differentiate the…

Q: Find all horizontal and vertical tangent lines for the implicity defined function x^2/4+y^2=1?

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Q: ; Find the equation of the tangent and normal line of the function f(x): V2x – 1 at the point (5,…

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Q: Find the equation of the tangent line to the curve y = Vx – 3 at the point (4, 1). - o y = }x - 3 2…

A: Explanation of the answer is as follows

Q: Find the point where the tangent line to y = x² at x 0.7 crosses the x-axis.

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: |Find the point(s) on the curve f(x) = x² where the tangent is parallel to the line 4x-y-1= (

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Q: Find the point(s) (x, y) on the function f (x) = V1+ 2x where the tangent line is parallel to the…

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Q: Find the equation of the tangent and normal line of the function f(x) =√(2x − 1) at the point (5,…

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Q: Find the slope of the tangent line to the curve x + xy – y = 23 at the point ( – 3, – 2). -

A: The given function is x2+xy-y3=23 The point is x0,y0=-3,-2

Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula…

Q: Find the slope of the line tangent to the curve y = sin' x at the point where x-x/3

A: We have to find the slope

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the slope of the line tangent to the curve y = sin x at the point where x = 3

A: Given: y=sin5x To find: The slope of the line tangent to the curve y=sin5x at the point where x=π3

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the derivative of 3 x +7 y = 8 dy %3D dx

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Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: Use the definition of the derivative to find the equation of the tangent line to the graph of y = Vx…

A: We write 6x+3y=4 in y=mx+b form to find slope

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

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Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: Calculate the gradient of the tangent line to the curve y3 - x3 -xy = 1at the point (-1,0).

A: