Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) < 6. = 2 and f'(x) > -2.

Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

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

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

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

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Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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

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Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: Find the derivative of the function by the limit process.

A: The given function is fx=-5x. Obtain the derivative as follows.

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: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

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Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

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Q: nd the derivative by the limit process (Gener x) = Vx2 - 4

A: In this question, the concept of the derivative is applied. Derivative The derivative is used to…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

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Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

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Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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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 the derivative of the function by the limit process. f(x) = −5x

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…