The function f has a continuous second derivative, and it satisfes f(2) = 5, f'(2) = 0 and f"(2) = -1. We can conclude that OA. f has a local minimum at 2. B. f has neither a local maximum nor a local minimum at 2. C. f has a local maximum at 2. OD. We cannot determine if A, B, or C hold without more information.

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

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

A:

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: To find critical point in which given function has relative maximum and minimum.Where…

Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

Q: (b) Argue that the graph of is decreasing for x near zero and that as x increases from zero, (x)…

A:

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the…

A:

Q: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

A:

Q: 10. f(x) = cos (2x)e*²-1

A:

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

A:

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: Please identify the critical point,z, where the first derivative is equal to zero for the following…

A: Critical point

Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

A:

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

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

A: We have to find which variable should we choose so that we differentiate as quickely as possible.

Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

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

A:

Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

A:

Q: s of 0 would be a minimum value on the graph of y = sin 0 over the interval [-27,0)?

A:

Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

A:

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 +…

A:

Q: What is (V and find the relative minimum point as indicated by the black dot on the graph at the…

A:

Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

A:

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: If c is a critical point and the derivative of the continuous function f (x) doesn't change from…

A:

Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

A:

Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

A:

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: Find the derivative, g' (x) for the function 1 t -dt 1+t3 g(x) = 3z+2 9z+6 1+(3z+2) (1+(3z+2)*)-…

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

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: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

A:

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

A:

Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

A:

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a