Consider the function f(a) = \x| on the interval [-2,2). 2 2. Since (-2)-f(2) = 0, there exists a value cE (-2,2) such that f'(c) = 0. -2-2

Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

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: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: By considering the derivative of the function f: [-1,1] → R defined by f(r) = show r2 +1' that f-1…

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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: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

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Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Consider the function f(x)f(x) whose second derivative is f′′(x)=9x+10sin(x). If f(0)=3f(0)=3 and…

A: We have to find f(x) and find f(3) using given intial condition

Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

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Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: Use the quotient rule to find the derivative. 2.1 +6 f(x) = x2.0 + 1 2.6 3.7 +2.1x x1.1 - 15.6x 1.6…

A: You need to just apply quotient rule.

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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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)…

Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

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Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: By considering the derivative of the function f : [-1,-1] → R defined by f(x) %3D r2 – x+1' 3. show…

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Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Consider the function f(x)f(x) whose second derivative is f''(x)=4x+3sin(x)f′′(x)=4x+3sin(x). If…

A: Consider the function f(x) It's second derivative is f''(x)=4x+3sin(x)If f(0)=3 and f'(0)=4   We…

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

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

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Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

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Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

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: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x<2b                     if x=21x-2-cx2-2x  if x>2…

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: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: 2- By using mumerical approximation ,the value of the derivative (f'(x)) in the table is true f(x)…

A: To find the derivative.

Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

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Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

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Q: Let f(x) =x. cos(x2). What is the correct result of the derivative of f with respect to x? =X•COS…

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