Determine if the following piecewise defined function is differentiable at x = 0. 4х- 1, X20 f(x) = 2 X + 4x – 1, x<0

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x² + 2x + 1…

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

Q: Evaluate the piecewise defined function at the indicated values. Sx² f(x) if x < 0 %3D lx + 7 if x…

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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: Let f (x) be a function satisfyingIf (x)| <x? for -1<x< 1. Show that f is differentiable at x = 0…

A: The solution is in step 2

Q: Use the definition of the derivative to show that the following function is not differentiable at x…

A: Given function, f(x)=9x It can be written as f(x)=9x,       if x≥0-9x,    if x&lt;0

Q: Is the function g(x) continuous at x = 5? g(x)= O No 1 5X+7, 5x-13, for x>5 Choose the correct…

A: Given query is to find function is continuous or not at x = 5.

Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: We first find the Right and left-hand limit of f'(x)

Q: Find the values of 'a' and 'b' that make the following piecewise function differentiable everywhere.…

A: We have to find value of a and b for given Questions.

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

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Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x&lt;1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: Find the derivative of the following functions using the limit definition. 1. f(x) = x² + 5x – 4 %3D…

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Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: sinkx) x 0

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Q: Differentiate the following function with respect to X. eX + 3Y =1

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Q: determine if the piecewise-defined function is differentiable at the origin.

A: Consider the given function fx=2x-1,                x≥0x2+2x+7,         x&lt;0 The left hand and…

Q: In the given question , find all functions f having the indicated property? The tangent to the graph…

A: Explanation: Given a function f(x) and point of tangency (x,y). Also given that, the tangent line…

Q: 1. Determine whether the following functions are continuous at the given point. a) f(x) = 1 ; а — 3…

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Q: Suppose that f(x) is a differentiable function such that f'(8)=7 and f(8)=1. If g(x)=cos(f(x)), then…

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Q: Determine if the given function is continuous at the indicated number x = c. |x-3| if x#3 4. j(x) =…

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Q: Determine if the given function is continuous at the indicated number x = c. 4-x 2-V 4, SE, if x+4…

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Q: Given the following function: y = x^4 - 8x^3 + 22x^2 - 24x + 2 on [0, 4], find the absolute extrema…

A: To find the absolute extrema of a continuous function on a closed interval [a, b]: Find all…

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f(x). If f(1)= 5 and f'(1)=10, then…

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Q: Determine whether the following functions are continuous at x = 2: x 2 7x + 3 f(x) = 3x + 7

A: Determine whether the following functions are continuous at x=2

Q: Determine the values of x at which the function in Figure  is: (a) discontinuous and (b)…

A: To determine the values of x at which the function is  a) discontinuous. b) nondifferentiable.

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: For f(x) = 4x? + 1, use the definition of the derivative, f'(x) = lim f(z+h)–f(z) h ,to find f'(x).…

A: We have to find f'x using limit definition of derivatives (quotient rule) where fx=4x2+1. We know…

Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: Determine if the given function is differentiable at a = 1 4 – 2x, if x 1

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Q: Find the constants "a" and "b" so that the following function sin 2x, if 0<xs. f(x) =- lax + b,…

A: Given f(x) is continuous and differentiable at x = π/6

Q: Suppose that f(x) is differentiable function such that f' (1)=8 and f (1)=4. If    g(x) = (f(x)) /…

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Q: Use the second derivative to determine the intervals on which the given function is concave up and…

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Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

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Q: Is the function given below continuous/differentiable at x = 3? %3D -3x + 2 x 3

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Q: Consider the following function. f(x) = V9 - x2 Find the derivative from the left at x = 3. If it…

A: Given that  f(x)=√(9-x^2)

Q: Q15 Consider the function f(x) : x2 + 5 4x – 3 f(x + h) – f(x) Use the definition of derivative…

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Q: Differentiate the following function with respect to x for y=2e^3x + 8e^9-2x .

A: Given equation is y=2e3x+8e9-2x Differentiate with respect to x.  then,

Q: Consider the piecewise-defined function f defined by f(x) = {1-4x 5 – 2x? if x > 1 if x <1 Find…

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Q: Determine whether the following functions are continuous at x = 2: 17x + 3 13x +7 x<2 f(x) = x22

A: In calculus, a function is continuous at x=a if and only if all three of the following conditions…

Q: Determine whether the following function is continuous at the given point z= 22 +9z – 5 f(=) = 2x-1…

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Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable. Show a…

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Q: 2. h(x) = at x = 1 x+1 %3D x2-1

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Q: Determine where the following functions are discontinuous, if anywhere. 0 x = 0 f(x, y): otherwise…

A: We need to find continuity of given function.

Q: 10.3.13. f(x, y) = xy ln(x² + y²).

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Q: Consider the following function. f(x) = -x2 - 10x – 9 Find its average rate of change over the…

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