(0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: 10. Find the equation of tangent line to the graph of f(x) = 2x – x³, at the point(-1, –1). %3D

A: Find your answer below

Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

A:

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

A:

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

A:

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: 4. Find the equation of the tangent line to the graph of g(x) = v2-x at x =-7 %3D

A:

Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

A:

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

A:

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

A:

Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…

A:

Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

A:

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

A:

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: . Find all points (x, y) on the graph of f(x) = x with tangent lines passing through the point (3,…

A: Tangent line has an equation of line with slope equals to derivative of the function at that point.…

Q: The equation of the tangent line to the graph of f(x) = vx+1 At the indicated point (3,2) is:…

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

A:

Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

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

A:

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

A:

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: 3. Find the equation of tangent line of the function f (x) = e" /x at the point æ 1. Write in the…

A: Given,  The function   fx = exx   We have to find the equation of the tangent line at the point x =…

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: Find the slope of the function F(x) = √√x+1 at the oint (8,3) And find the equation of the tangent…

A:

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: 3) Find the slope of the curve defined by f (x) = x 3 sin x at x =r.

A: Solution -  Slope of the curve is given by df(x)dx, We have the function f(x), f(x) = x3sinx, Now…

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

A:

Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: A curve y = f(x) defined for values of x > 0 goes through the point (1, 0) and is such that the…

A:

Q: find the line tangent to the curve y=cos(x) at the point (π/4, 1/√2)

A:

Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: 2 Consider the curve given by f(x)=x²³x + 5 find the equation to the tanget to the curve at point…

A: We know that a line which touches the curve fx at one and only one point is called a tangent line.…

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…