Use the definition of the derivative to determine whether x < 0 0 < x < 1 1 < x < 2 (10x2 + 41, x > 2 x, f(x) = is differentiable at x = 2. x2 + 5,

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Use the definition of the derivative to find f(x)

A: To find: The derivative of Fx=5x2-3 by definition of derivative: Concept used: Definition of…

Q: Use definition to compute the derivative of f(x)= V3x+1. You may not use any calculus formulas.

A: Use first principle.

Q: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

Q: The derivative of (x3 - 4x)&gt;x is obviously 2x for x  0, because (x3 - 4x)&gt;x = x2 - 4 for x …

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Q: The derivative of the function f(x) = In 5x is 1 x In 5 Select one: O True O False

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Q: h) f(x) = Write your answer in simplified factored form. %3D

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Q: Show your work to determine the derivative of f(x) = (-1/x2 + 1/2 x2)(√x - 3x4). Do not simplify…

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Q: 4) Find the derivative of f(x) = (5x² - 3)² in two different ways.

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Q: 2. Find the slope of the graph of the function f(x) = 9x² - 4x5 at x = -1. Show your work using the…

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Q: What is the third derivative of the function: f(x) = x5 - 4x³ + 3x?? O 5x – 12x² + 6x O 20x? 24x + 6…

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Q: Find the derivatives of the function f(x) from the first principle x*+4

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Q: Q3. Derive the following formula for approximating the derivative f": ƒ™" (x) ≈ (f(x +3h) − 3f (x +…

A: To Derive: f'''(x)≈1h3f(x+3h)-3f(x+2h)+3f(x+h)-f(x). To find: Big-Oh error term from the above…

Q: Suppose that f: R → R is a function with second derivative f"(x)=x•(x+ 1)³ · (x + 5)ª . Find…

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Q: If f(x)= anx", specify the domain of f.

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Q: Find the error that was committed below when taking the derivative of f(x) = Dx 3x+10 3(x²+3)+(3x +…

A: NOTE: Refresh your page if you can't see any equations. . take derivative use the quotient rule…

Q: The slope of the tangent line at any point on the graph of f(x) = 7x2 + 4x is given by the…

A: Given f( x ) = 7x2 + 4x f'( x ) = limh→0f( x + h ) - f( x )h

Q: Q2. Derive the following formula for approximating the derivative f": ƒ"(x) ≈ : (-f(x+2h) +16f(r+h)-…

A: To show:- f''x ≈112h2  -fx+2h + 16 f(x+h) -30 f(x) +16 f(x-h) - f(x-2h)

Q: F(x) = X2

A: Consider the function: fx=x2 The derivative of f(x) with respect to x is the function f′(x) and is…