Let f(x)= squareroot of (7x+11) . Find a general equation for the line tangent to f at x=a where a≥ -11/7

Q: Find the equation of the tangent line to the function f(x) = x3 + a2 – x – 3 at the point where x…

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Q: Estimate the slope of the tangent line to f(x) = x³ at x=2 by finding the slope of the secant line…

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Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: Determine the equation of the tangent line and the quadratic approximation to the function z = e2"…

A: Given function is: z=e2x To find the equation of the tangent at a point x=x0 to curve y=fx,…

Q: ) Find the equation of the tangent line to f(x)= (36+2x2)-1/2 at x=0  y= (b) Use your answer to…

A: We use the fact that f(X) is approximately equals to f(a)+ f'(a)(x-a), which is tangent to line to…

Q: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: Find the equation of the tangent line to f(x) = 2x* – 5xat x = 1. - Oy=3x+10 Oy=6x+19 Oy=6x-9 O…

A: Given equation: f(x)= 2x4- 5x f(1)= 2(1)4- 5(1)= -3

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

A: See the attachment

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: Find all the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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Q: The equation of the tangent line to f(x) = 5x2 + 7 at x = 0 is a y = 5x + 7 b y = 7 y = 2x + 14 O d…

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Q: At what point on the curve y = V-8 + 2x is the tangent line perpendicular to the line 8x + 4y = 1?

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Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the slope and equation of the tangent line to f(z) = 5- 2z at a = 2 using the definition.

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Q: What is b > 0 if the tangent line to y = bx at x = 0 has slope 2?

A: Our Aim is to find thr value of b given that the tangent line to y=bx-(i)at x=0 has slope 2.

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: Find the equation of the tangent line to the function f(x)=x3+x2−x−3 at the point where x=−2.Select…

A: We have been given a polynomial function as shown below and we are supposed to find equation of line…

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: Find a function f such that f'(x) = 2x' and the line 54x + y = 0 is tangent to the graph of f. (x) =

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Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find an equation of the tangent line at x and f'(3) = 2. 3, assuming that f(3) = 5

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Q: Find all points on the curve y = x3 + 2x2 -6x +5 where is the tangent is parallel to the line 2x + y…

A: The given curve y=x3+2x2-6x+5

Q: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find a point on the curve y=x2−2x−3 at which the tangent is parallel to the x−axis.

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Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: The value of b makes the liney = 2x + b be tangent to the function f (x) = x² is

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Q: Find the equation of the tangent line to the function f(x)=−2x3−4x2−3x+2 at the point where x=−1.…

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Q: Find the equation of the tangent line to the function f(x) = -3x – 2x2 – 1 at the point where x =…

A: Given : fx = -3x3 -2x2 -1

Q: Find the equation of the tangent line to  f(x) = x2 − 2x + 2  at  x = 5.

A: The given equation is fx=x2-2x+2.

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: Find the equation of the tangent line to f(x) =3cscx+xsinx at X= 2 A y=x- 3 y=x+3+ 2 y=x+3 y=x+3-

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Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: Find the equation of the tangent line to the curvef (x) = 2x³ 3. - x at x = 2. o T(x) = 14 – 23(x –…

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Q: Find all r-values where f(x) = (x2 + 2x - 3)4 has a horizontal tangent line.

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…