Show that f(x) = x3 - 2x - 1 has a real zero between 1 and 2.

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

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Q: Determine all critical points of the function f(x) = 2x(4- x)³.

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Q: What is derivation of f(x) = (2x² – x + 1)³ at %3D Xo = 1 ?

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Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

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Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: fG)=4x-3 SC) = (f of ) (x)=

A: Given fx=4x-3.

Q: Find the absolute extreme of f(x)=x^3-12x on the closed interval [0,4]

A: for finding critical points take f'(x) = 0 then find the function value at the critical points and…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A: The function is given by f(x) =-2x3+6x2-3 To evaluate : The point of local maxima or local minima.

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

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Q: find the extrema of f(x) =2x3-6x on [0,3]

A: Given:

Q: 2. Calculate the point(s) of intersection of f(x) = 2x² + 4x – 11 and g(x) = -3x + 4.

A: Given f(x) = 2x2 + 4x - 11 and g(x) = -3x + 4

Q: The function f(x)=(2-x)/(3) is continuous at

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Q: Use the intermediate value theorem to show that the equation x + 2x + 1 = 0 has a solution in the…

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Q: 5. Use the Intermediate Value Theorem to show that the function f(x) = x³ + x² – 1 has a zero…

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: Find the absolute extrema of f (x) = 2x – 3x² – 12x +1 on the interval [-3,3].

A: fx=2x3-3x2-12x+1 Differentiating with respect to x, we get f'x=23x2-32x-121+0=6x2-6x-12 Now to find…

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: Show that the function f(x)= x^3 − 15x + 1 has three zeros in the interval [−4, 4]. Do not solve for…

A: The given function is f(x)=x3−15x+1The interval is [−4, 4].To show that f(x) has three zeros in this…

Q: Show that f(x) = 3x². x is not differentiable %3D

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Q: Find the positive critical point of the function f (x) %3D x4 + 7 x =

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Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1

A: Given that: f(x)=x2+2x-3x-1

Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

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Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Intermediate Value Theorem : The theorem states that for a function f continues on [a, b], if f(a)…

Q: DERIVE THE F. FUNCTIONS: s) y (x-3)(3x+4)(x²-2x+ 1)

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Q: Find the absolute maximum and minimum of f(x)=3x^3-x+1 on the interval [0,1]

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Q: 6. Obtain the TSE of f(x)=2x-² in powers of (x-1).

A: Solution is here

Q: Explain why g(x) = f(x), if x ≤2 0, if x > 2 is not differentiable at x = 2.

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Q: Find the absoltute extrema of the function f(x)=x"-32x+256 on the interval-5,5

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: Find the absolute extrema of f(x) = 2x3+3x2−12x on the interval [0, 2]

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Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

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Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Explain why f(x)=3x^2+1 is continuous at x=-2

A: Consider the function  f(x)=3x2+1

Q: Find f for the function z = - 3x6 0 02-30x4 ex ax = ex 7x8 1 8 6x 02-02-63 x = 6xy + 4y2.

A: This question can be solved using the concept of partial derivatives.

Q: 13. Use the Intermediate Value Theorem to show that f(x) = 2x° – 3 has a zero in the interval [1,2].…

A: Given:-f(x)=2x3-3 using the intermediate value theoremf(x) is continuous in the interval 1,…

Q: Find f'(x). f(x) = In x +3 eX – 4x² %3D

A: f(x)=lnx+3ex-4x2Differentiate with respect to xf'(x)=ddx(lnx+3ex-4x2)=1x+3ex-(4×2)x=1x+3ex-8x

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x>2 To find the continuity of the…

Q: Use the Intermediate Value Theorem to show that f(x) = 2x3 − 3 has a zero in the interval [1, 2]

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Q: What are the critical numbers of the function f(x)= 2x^(3)-2x^(2)-16x+1?

A: Let's find.