4. Use the first and second derivative to find the absolute maximum and minimum, if either exists, for (x) = -x' + 2x' on (-x,) on

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: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

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Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

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

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Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

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. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: 5. Find the equation of the tangent line to the curve of the function Y= 2x-x +2 at the point (1,3).

A: Given,  y = 2x3-x2+2   and the point 1, 3 We have to find the equation of the tangent line at the…

Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

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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: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

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Q: Find f(x) if f(2) 5 and the tangent line at x has slope (x = 1)eX- 2x. %3D f(x) =

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Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: The derivative of y= sech-(Inx)+e sinh- (3x) equals Select one: +3esinh (3x) cosh(3x) y' = xlnxv…

A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: In (In e*1): What is the derivative of y 3z²+1

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Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

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Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

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: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: y = e* (In x)² %3D

A: Here we want to find the first derivative of the given function. For finding the derivative we use…

Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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: What is the value of the first order derivative of the closed function given as…

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Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

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Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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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: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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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. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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

A: Given: y2=x…

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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

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Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

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…

Q: 4) Determine the equation of the tangent line to y=3x -5x² +10 at x= 1

A: The given equation is; y = 3x4 - 5x2 + 10  at x = 1