If f^(x)=c for some natural number n and constant c, then f is a polynomial function. True or false?

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

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Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

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Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: We exclude from a function’s domain real numbers that result in a square root of a/an________…

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Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

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Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

Q: If the bound of error greater than zero, the polynomial is------than the .function not equal O its…

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Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: Which are important types of functions are frequently encountered in calculus?

A: Important types of functions frequently encountered in calculus can be categorized as follows:Based…

Q: Use derivative rules to compute f'(-1) given f (x) = -4x8-32x - 4.

A: f(x)=-4x8-32x-4Formula: xn'=n xn-1

Q: How to find derivative of polynomial?

A: To find the derivative of any polynomial function use this formula:       the derivative of…

Q: tion 1. Find the rule of the piecewise function

A: 1. From the graph given , the piecewise distribution of the function is as follows ,  fx=x+1 ,…

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: Find the 도ite d Point of the Folowing Functionse 2. x3

A: Given function is F(x) = x3 + x2 - 9x + 8

Q: Differentiate the function. 3. %3D In(x)

A: Given y=3ln(x)differeniatey'=ddx3lnxy'=3ddx1lnxApply exponent rule:  1a=a-1y'=3ddxln-1xApply chain…

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: What is the average rate of change of the functin g(x) = 2x^2 -9 on the interval [4,7]

A: g(x)=2x2-9 on the interval [4,7]

Q: if cosh(x)=41/40 and x > 0, find the other hyperbolic functions of x

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Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: theoretically define what is the derivative of a transform and what is its function

A: Given data is : Define what is derivative.

Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1]

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Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: True or False The cube root function is odd and is decreasing on the interval (-∞,∞).

A: we have to tell whether the given statement is True or False

Q: We exclude from a function's domain real numbers that result in a square root of a/an number.

A: Given: We exclude from a function's domain real numbers that results in a square root of a/an _____…

Q: Use secant method to estimate a root for function f(x)= x3 + 2.7x+ 2.6 = 0, starting for interval…

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Q: What are the variety of important types of functions frequently encountered in calculus?

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Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: det fi s→ IR be afanction and 8= [-202] 5-+ $$ f(x) = -25x2-1 -15x20 3 05341 2 1<x<2 ร

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Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: All polynomial functions are continuous. * TRUE FALSE

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Q: The derivative of f(x) = ax² will be greater than that of f(x) = ax, for a domain of (0,1), where…

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Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…

Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A: NOTE: Refresh your page if you can't see any equations. . the total length of the wire is L=8x so…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11…

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Q: Give the result of every step in using the 4-Step Rule to find the derivative 14. f(x) = x3- 4x² + x…

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Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: How do I find th end behavior of f(x)=-(x+1)^(2)+4

A: f(x) = -(x+1)2+4 =-x2-2x-1+4=-x2-2x+3

Q: How to solve this problem from webassign by deriving to find f'(x) f(x) = 4x^2 ln 4x

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Q: Prove the product rule for differentiation of real valued functions.

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Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below