и(х) -f(x) 1(x) 1.5 + 2 3 4 In the figure, is f(x) squeezed by u(x) and (x) O 1. at x = = 3? ? 2. at x = 1?

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: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

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: 4. Find the local maximum and minimum values of f, using both the First and the Second Derivative…

A: The given function is fx=x2x-1. Compute the critical points as follows.…

Q: 7 Determine a value for r so that h(x) x + rx² – 7x has an inflection point at x = 5. 2 -- |

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Q: 2/3 Determine where the absolute extrema of f(x) = 3x25 - 2x on the interval [-1, 1] occur. The…

A: To find the absolute extrema of f(x) check the values of f(x) at critical points and at the end of…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: The function is given here, For maxima minima, So, the function has only one extrema in its…

Q: 64 8. f(x) dx = 14, find xf(x?) dx. If f is continuous and %3D

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Q: Sx' - 3, xS2 lx² +1, x>2 a. Is h continuous at x = 2? b. Is h differentiable at x = 2? 2. Given that…

A: A function is continuous at a point if the limit of a function at that point is equal to the value…

Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

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Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

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Q: x2 Consider the function f(x, y) = 2y lim (x,y)(0,0) f (x,y) does not exist by using e – 8…

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

A:

Q: 73 9x +4 then f(x) has a local maximum at the point 3 Use second derivative test, If f(x) %3D - O…

A: Topic:- application of derivatives

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

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Q: a) For the function f(x) =1-3x? , find f'(a) at a =-1 by using the definition of derivative. (a+b b)…

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Q: 12. Consider the function f(xx) = 2x² + y* + 4xy. %3D (a) Find the critical points for this…

A: Find the critical points of the function fx,y=2x2+y4+4xy

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given:   To determine: The antiderivative of f(x)

Q: 9.) f(x) = (2x + 1)* %3D

A: The integration technique to calculate the first derivative is:∫(ax+b)n-1…

Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: Consider the function f(x) = x – 3 ln(x), <x< 5. The absolute maximum value is and this occurs at x…

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Q: 8.) f(x) = v5x* – 12

A: Given:        fx=5x6-12        fx=5x6-1212 differentiating on both sides    f'x=ddx5x6-1212

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

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: 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: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: Consider the function f(x) = x – 3 ln(x) on the interval 3 The absolute maximum value is and this…

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Q: 2-(i) Suppose that we know that f(x) is continuous and differentiable on [6,15). Lets also suppose…

A: 2) Suppose that we knw that f(x) is continuous and differentiable on[6, 15]. Also, suppose that we…

Q: Find the absolute maximum and absolute minimum values of the function f(æ) = 2x – 15 In(3x) on the…

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Q: 5. Evaluate f(0) when f(x) = 2 tanh x. А. О В. 1 e²+1 2e D. -1 E. None of the above 2e

A: To find f(0)

Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: 2the second derivative test to find the loscal maxilnum and minimulin of thie functioni 3 f (x}こ 2メ2…

A: To find the local maxima and local minima of the below function. fx=2x3−3x2−12x

Q: 3.) if f(x)= akw f(x) = x-1 and (X) X-1 What is the valule of

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

A:

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: dx For = In[F(x)]+C•What is f(/3) if C = 0? (x+x³) (x Tan-lx+ 1) -1 + - - 3. -1 + - + S-is-isS

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Q: 8. x' + 10x² + 6x + 4 is concave down. 3 Determine the interval(s) at which f(x) = -- a) O(-1, 00)…

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Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: x² +2x+1 6.) f(x) = 3

A: The given function is f(x)=x2+2x+13. Find the first derivative or f'x of the functions by using the…

Q: 43 31) Describe all y=flx) which are defìned for all XEIR and satisfy continuoUs functions ə47…

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Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…

Q: 4. Using the expression (x + Ax)² = x" + nx-Ax +n(n – 1)x"-²Ax² + + Ax" ... prove that if f = ax"…

A: