Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x) at (2,5) has slope 3, then the tangent line to the graph of y= f-'(x) at (5, 2) has slope.. O 3 O -3 O 1/3 O -1/3 O 1/5

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

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Q: 8z 4. Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

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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).

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Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: 4. Find an equation of the tangent line to the curve of f(x) at the given point. 2x + 11 (a) f(x)= =…

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Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 2. Find the equation of the tangent line to the curve y = In(x'-7) at (2,0).

A: Given :          y=lnx3-7

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Q: 7. Find the equation of the tangent line (in the form y = mr+b) for the function f(x) = In(x-3)+6V…

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Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: 9. Find the slope of the tangent line to the graph of f (x) = sin (cos 2x) at x = 1 A. -2(sin 2)(cos…

A: we have to find the slope of the tangent line to the graph of fx=sincos 2x at x=1

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: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

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

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Q: Suppose the function f(x) has the derivative f'6): 4x-122 -8 こい x-) G。 C) what are the x-values of…

A: Here given derivative of function f(x) as f'x=4x-2x+12 (a) To find the critical point of function…

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

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Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: 3. Let f(x) =x In(x – 3)+5. Find the equation of the line tangent to the graph of f at the point…

A: Given thatf(x)=xln(x2-3)+5f'(x)=ddxxln(x2-3)+5         =xddxln(x2-3)+ln(x2-3)ddx(x)+ddx(5)…

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

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

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Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

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A: Given that:y=ln1-xx+35To find derivative

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

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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: Suppose that f is a differentiable function with f(2) = 5. If the tangent line to the graph of y =…

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Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

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

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

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: 1. If f(x) = (2x)cosx, then f'(x) =?

A: Dear student as per our rule in one session we can only solve one question please post the other…

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

A: Given: y2=x…

Q: 5. Find the tangent line to the curve of f(x)= Vx2 +8x at x = 1.

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Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(x) = V5x +1. V5yl th)-…

A: Given; f(x)=√(5x+1)

Q: 1. Find the equation of the tangent line to the graph of f (x) = x²e-* at x = 1. %3D

A: The given function is: fx=x2e-x In order to find the slope of the given function, find the…

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1 What…

A: equation of tangent is y=4x-5 therefore equation of curve whose tangent is y=4x-5 ,…

Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

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

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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