Prove that constant function is differentiable at ever x ER.

Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: Give Three Functions  of Wronskian ?

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

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

A: We have given function fx=e-x As we know the modulus function is not differentiable at x=0.…

Q: Is there a real function f(x) that is differentiable only at a point x?

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Q: the function f is not differentiable at x=0.

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Q: Find all critical points of the function. f(x) = x lnx

A: A critical point is a point on the function curve at which the derivative equals zero or the…

Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

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Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

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Q: Show analytically that the function f is not differentiable at x = x² x1

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Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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

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Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: Lat f be a continous and differentiable function. If f'(c) = 0 then c is a local maximum or local…

A: Answer

Q: Let g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

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Q: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: Find all antiderivatives of function:  f (x) = -4x

A: An antiderivative of a function f(x) is the indefinite integral ∫f(x)dx. Denote this antiderivative…

Q: Determine if the function is continuous at point (0,0): F(x, y)=**y°cos(x*+y³) (x²+y²)2

A: Given that Now take x=0, Now take y=0,

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

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Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Let 'f be a continuously differentiable real valued function defined bx + a by f(x) ={ 5x x<1 x21…

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Q: Is the function f(x)= x+|x|-1 differentiable at x=0.

A: Consider the given function:

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: If two functions Fand G are both antiderivative of the function h then they differ by a constant.…

A: Integration of h is F and also integration of h is G. So, F' = h  And, G' = h

Q: Determine if the function is continuous at point (0,0): F (x, y) _x³y°cos(x³+y³) (x²+y²)²

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Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

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Q: Solve for a and b that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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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: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Indicate all critical points of the function f(x)=∣∣x2−5∣∣.

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: . Use calculus to find the absolute maximum and minimum value of the function f(x)= x+ cos x on the…

A: Consider the function: fx=x+cosx,  0,π To calculate the derivative of the given function with…

Q: Find all critical points of the function f(x)=xlnx.

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

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

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Q: Find the intervals on which the function is continuous. f (x) = { %3D 3, x = 2

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Q: F(x) = (3t +2) dt +2

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Q: Prove that the function f(x) = cos x is strictly decreasing on the interval [0,1]. %3!

A: 5) Given that, fx=cosx

Q: Let be a differentiable function such that f(3)=2.345 and f'(x)= ln(x^2+1).What is the value of…

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

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Q: Decide whether or not the real function In (cos 2x) 2x2 x + 0, f(x) = -1, = 0, x = is continuous at…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: 1-What are Univalent Functions .

A: We define a function on complex numbers.

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: Use the chain rule to show that for any differentiable function f(x) > 0, f'(x) [In(f(x))]' = f (x)"…

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