12. Let f (x) = sin x On [0, 27) the maximum value(s) of the function occur(s) at what x-value(s)? TT 2T

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x<πmx+b,      x≥π Since the function fx is continuous…

Q: What is the maximum value of y = cos x. For -5 < x <? 1 2 O 1/2

A: Topic = Derivative

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

A:

Q: 2. If f is differentiable at a, then Duf(a) = Vf(a) · u. Moreover, if Vf(a) + 0, it gives the…

A:

Q: If f(x)= 2- cos(x) sin(x) then the absolute minimum of f on the 3T interval | 프,프15: 4 O 2/2-1 O…

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: Q1. Differentiate the following functions with respect to x: i. y = x-% -4/x ii. y = x+Inx+ sin(3x)…

A:

Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 6) Suppose f (x) is a differentiable function such that f (1) = 7 and f'(1) = 2. Use a tangent line…

A: This question is based on deduction of straight line using given information.

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for…

Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

Q: II. Let F(x)= ecosh z √x+1 1. Find F(0). 2. Find F'(x). sin(1-t) dt.

A: Let Fx=∫x+1cosh x sin1-t dt.1 To find F0.2 To find F'x.

Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: 3sin-1x, if -1< x< 0 f(x) = x2+ Tt if x20 x+cosx'

A:

Q: 6. Suppose that ƒ is differentiable on (a,b). interval [a, b]? Justify your response for find a…

A:

Q: 8 Consider the function y= f(x)= a) Find the quintic (degree five) approximation to f(x) centered at…

A:

Q: Consider the function f(x) = sin(xª(1 – x)') with a, b > 0. We know that: %3D f is differentiable at…

A:

Q: Find a and b which make the following function differentiable at x = 0; ax+b, x < 0 sin x, f(x) = =…

A: We know a function is differentiable if and only if Right hand derivative and left hand derivative…

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

A:

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

A:

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x&gt;0

Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: Q1: From the given graph of f(x) = sin x; [0 ,27] , f ind: (a)The critical points. 211 -2…

A:

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

A:

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: Find all local minimum and local maximum value(s) of the function. f(x) = 2 cos x – sin? x, 0< x< 27…

A: Option 4

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

A:

Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

A:

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 2. The following funchion O, x = 0 flad = f(x) |-X, 0<x<l is differentiable on (0,1) and satisfies…

A:

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

A:

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given, w=f(x,y) x=rcosθ and y=rsinθ

Q: 5. Find the exact absolute maximum and absolute minimum values for 2 f(x) = cos(x) + sin´(x) on the…

A: We have to be find

Q: Find the absolute extrema of the function on the closed interval. f(x) = cos TX, [] minimum (x, y) =…

A:

Q: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

A: Given function is f(x)=1sin πx4 over the interval 0, 1 and  q(x)=4x+32x2-1 Extreme value theorem: If…

Q: if z=0 ne function f(z)= )² if z+0 is differentiable at z= 0 LL

A:

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: 1. Verify whether the function f(2) = e=Y sin x – ie- cos x is entire or not. 2. Show that the…

A: Given: Let us consider the given, 1) fz=e-ysinx-ie-ycosx 2) fz=xy+iy

Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &amp;  f"(x)=12x2