3. Let f be a function. f is even if f(-x) = f(x) for all x in domain of f. f is odd if f(-x) =-f(x) for all x in the domain of f. Using the above definitions, determine whether the function f(x)=3x' + 2x² is even, odd, or neither.

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A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

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A: Consider the function

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A: fx=x32

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

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A:

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

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A:

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A: Given : hx = fgxg-1= 2g'-1 = 3f'2 = -4

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A:

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

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A:

Q: For what value of the constant c is the function f continuous on (-∞, 00)? cx2 + 2x if x 2.

A:

Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

A:

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

A:

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

A:

Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

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Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

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Q: ,for x 1 Discuss the contuniuty of f andf'.

A:

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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Q: +1 Differentiate the function f (x) = In +1

A:

Q: 12. Use the definition of increasing to argue that f(x) = x5 is increasing on all of R. Then use…

A: The increasing of a function indicates that the value of the function increases with the increase of…

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

A:

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

A:

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

A:

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

A:

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

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Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

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A:

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: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

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A:

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

A:

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

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

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A:

Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

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Q: Suppose f is differentiable with f(0) = 0 and 0 0.

A:

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A:

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)