If f(1) = 12 and f '(x) 2 2 for 1 < x < 5, how small can f(5) possibly be?

Q: Find the derivative of the function by the limit process. f(x)= 2/x2

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Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

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Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: Find the general solution using reduction of order. 1. y''=ln(x)

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what is…

A: Given: The derivative f'x=x2+2sin2x-2 and f2=7 Find the absolute minimum value of the function over…

Q: Find the derivative of f(x) = 1 at x = 3

A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1

Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

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Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: 3. Solve the first derivative of f(x) = evx at x = 0.5 using centered finite-divided difference and…

A: To find the first derivative of f(x) at x=0.5 using centered finite-divided difference and a step…

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: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: Sometimes the second derivative test is harder to use, even if it applies. Use the first derivative…

A: Given,

Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: 7.) f (x)> (3x+2)(5x-2)

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Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

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Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

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Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

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Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

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Q: Find the absolute maximum value of ƒ(x) = x2 ln (1/x) and say where it occurs.

A: We need to find the absolute maximum value of the function

Q: 1 Find the function whose derivative is (x+1)-

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Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: 5. y=x3 Find derivative ldv 4.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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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: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

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: 1. Show a numerical method of approximating the instantaneous rate of change at x = 3 for the…

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

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Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

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Q: The approximation of the root x* of the function f(x) = ln(x + 1) - x + 3 accurate to within 10-2…

A: Introduction: Another recursive technique for approximating the polynomials' roots is the secant…

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…