Suppose that f is differentiable on some open interval containing c, and (c,f(c)) is a point of inflection of the graph of f. Then f"(c)=0.

Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: If f is continuous but not differentiable at x = c then there is a corner on its graph at (c, f(c)).…

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Q: If f is continuous at a number, x, then f is differentiable at x. True

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Q: Find an example of a function f:[0,1]¬R such that f is not continuous, but f does satisfy the…

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Q: Let f be a differentiable function. Consider the relation = x•f where z is implicitly defined in…

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Q: Please

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: If f is differentiable at a number, x, then f is continuous at x.

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Q: If f(x) is continuous in the interval [-2, 1], ƒ(−2) = −4, and f(1) = -1, can we use the…

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Q: 18. Suppose that f is a differentiable function such that f(g(x))= x, and f'(x)= |3D 1 1+(f(x))².…

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Q: f(x)={x^2−9x≤c, 2x−10 x>c } i

A: Consider function f(x)=x2-9           x≤c2x-10        x>c Now  limx→c+ f(x)=limx→c+…

Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: Suppose f is differentiable on some open interval containing e and f" (c) = 0 then (c, f(c)) is a…

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Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: Let f be a differentiable function such that f(4) = 3 and f'(x) = -3x + 3. What is the approximation…

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Q: Suppose that f (x) = x·g(x) for some function g that is continuous at 0. Prove that f is…

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Q: Let f(x) = x²+x+ 2 = Z₂ (x) prove that f(x) irreduciable Poly

A: The given function is  f(x)=x2+x+2.

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

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Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

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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: Prove that f (x) = x-12 is : (i) not sectionally continuous in every finite interval in the

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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?

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Q: (a) Let x2 if x is rational f (x) = 0 otherwise. Prove that f is differentiable at 0.

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Q: Suppose that a function h satisfies −x^2 ≤ h(x) ≤ x^2 for all x. Prove that h is differentiable at x…

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Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

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Q: Can Rolle's Theorem be applied to f(x) = 1/(1-x) on interval [0,3]? If yes, what is c in (0,3) such…

A: here we can't apply the rolles Theorem

Q: Suppose that f : R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the 8–neighborhood…

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Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

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Q: Consider the function f with domain (-2, ): 3|x2 – 1| 2x2 + 2x – 4 if – 2< x < 1 f (x) = 3 if x = 1…

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Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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Q: Suppose f and g are differentiable functions on R such that,

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Q: Let f be differentiable on an interval A. If f'(x) not equal to  0 on A,show that f is one-to-one on…

A: Given that, Let f be differentiable on an interval A. If f'(x) not equal to  0 on A. We have to show…

Q: Define f(2) in a way that extends f(s) = 2 to be continuous at s = 2. %3D -4

A: The function is defined as fs=s3-8s2-4.

Q: 2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is…

A: Given query is to find function is continuous or not at x = 1.

Q: Suppose that u(x) is a differentiable function such that

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: 5.Prove that: if f is continuous at x = 0, then xf (x) is differentiable at x = 0.

A: We want to prove the given result.

Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: If f is differentiable at a ,then f is continuous at a

A: Every differentiable function is continuous.

Q: + The f(x) = Undefined at x = -3 %3D TO F O

A: Given: f(x)= x-13-x A function is undefined at a point x=a, if the denominator of f(x) is 0 at x=a

Q: Suppose f is a differentiable function on an interval II and f(x) 6= 0 for every x in the interval.…

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Q: (2) Find an example of a function f : [0,1] → R such that f is not continuous, but that f satisfies…

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Q: Show that the function f:R to R defined by f(x)=5x-12 is continuous using the E-d definition

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Q: Consider the function f with domain (-2, 0): 3|a2 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: Show that f : (0,∞) → R defined by f(x) := 1/x is not Lipschitz continuous.

A: Definition:  Let S⊂ℝ and a  function f:S→ℝ is Lipschitz Continuous at x∈S if there is a constant C…

Q: Prove that the function f : R → R given by f(x) = 3x° – 2x is continuous at 1 using the a.…

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Q: Prove that there is no continuous function f : S² → S' such that f(-x) =-f(x) for all x € S².

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