Consider the piecewise-defined function f defined by 8 -3x2 11 6x { if x 1 if x 1 f(x) Find f'(1). Iff is not differentiable at the number c = 1, enter DNE f'(1)

Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Suppose the function f(x) has the derivative f'6): 4x-122 -8 こい x-) G。 C) what are the x-values of…

A: Here given derivative of function f(x) as f'x=4x-2x+12 (a) To find the critical point of function…

Q: Find the global maximum and minimum of the function on the given…

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Q: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: x2 f (x) = t² sin(2t) dt 1

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Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x&lt;03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

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Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

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Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: Find tangent line for the following f(x) = ( 4x² – 3)² f(x) = sin(8 x) at (7, 0) and (T, 1). 9. at…

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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Q: n(x)=3x?4k+1 %3D

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(x) = V5x +1. V5yl th)-…

A: Given; f(x)=√(5x+1)

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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