1. Find all critical numbers of f(x) = x³ ln(x). (a) e5 only (b) e-1/5 only (c) e and 1 only (d) e only (e) no critical numbers 1A 1B 1C 1D 1E

Q: 1. (a) f(0) = ln(sin 0) + sin(ln). (c) y = ln |x³ - x²| Find the derivative of each function. (b)…

A: Note:-Since you asked multiple sub parts questions , according to our policy we can answer only…

Q: Use the following table of values to answer (a) and (b) a)  Let h(x) = f (g(x)) . Find h'(2) .…

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Q: Find the critical numbers of f(x) = ln(x2 + 5x + 14).

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Q: (2) Show that f(x) = e³x cos(2x) is of exponential order.

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Q: If f(t) = 103t-5 x e2t, determine the value(s) of t so that f'(t) = 0.

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Q: 1 g(x) (1 – x)3'

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Q: Let f and g be two functions having continuous second derivative on the interval [a, b). Its given…

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Q: The 2nd derivative of y = 24r is A 2*+2 In(8) B 2tr+4 In(4) © 24r+4 In(2)

A: Given that: y=24x

Q: a)If h(x)=f(3x) then  h′(2) b) If  y=f(x2+2)  then  y′∣x=1= c) If  G(x)=cos(f(x)) then  G′(π)=

A: Topic:-Derivative

Q: If g(x)=5*, then g'(2) is:

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Q: Determine E (X) and V(X) x -1.0 -0.5 0.5 1.0 a. E(X) = 1/8 V(X) = 0.4219 b. None O c. E(X) = 0 V(X)…

A: E(x) = (-1 x 1/3) + (-0.5 x 1/6) + (0.5 x 1/6)             + ( 1 x 1/3)        = (-1/3) + (-1/12) +…

Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: 4. Let the pdf for X be f (x) = where C is a constant you have to determine. Let X(x) = Cx for 0 < x…

A: The constant C can be obtained as follows:

Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: H.W prove * (f -g)'(x) = f'(x) – g'(x)

A: According to bartleby guidelines we are allowed to solve only one question at a time. So kindly…

Q: Using False Position Method, get the roots of the following equations. Show your solution via excel.…

A: See Answer below

Q: The critical values of f ( x ) = x 2 e − x 2 are?

A: Given, f(x) = x2e-x2      Critical point of function is a value of X in domain of function at which…

Q: Let k(x) = (4x²)g(x)h(x). Given the following table of values, find k' (1). -1 1 1 0 1 -4 0 2 1 -1…

A: The given function is .To find the value of .Derivative formula:

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Q: y'(x) = P(x) + Q(x) * y(x) + R(x) * y (x) P(x) = -e2** ricatti dif. Q(x) = 2 R(x) = e-2*x

A: The given Ricatti's differential equation is                    y'(x)=-e2x+2y(x)+e-2xy^2 ⋯⋯⋯⋯ (1)…

Q: 2. (a) Find the critical point(s) of P(x) = (x - a)(x – b) . The letters a and b denote constants.…

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Q: 2. Use chain rule to find the derivative of the following functions (Hint: for function composed…

A: NOTE: Refresh your page if you can't see any equations. . Since you have asked multiple questions,…

Q: Halley's method is an improved Newton's method where the second derivative of a function f (x) is…

A: Halley's Method: The formula to find the root of f(x) is given as…