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Q: Give the value(s) of x at whichf has either a local minimum or a local maximum. Give the interval(s)…

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Q: The value of (i)* is = O e^(-T/2) e^(T/2) O 1/2 -T/2

A: The solution is given as

Q: polmto The value of (i)" is = O T/2 O -T/2 O e^(-Tt/2) e^(T/2)

A: Solution ) i = cos π/2 + i sin π/2  i = eiπ/2 i-i  = e(iπ/2)(- i ) i-i = e-π/2 (i × i ) [ i × i = -…

Q: .......

A: To find one x value where f'(x)=0. That is the tangent at x is parallel to x-axis.

Q: 1) The distance, travelled by a car, f(x), in meters, after x hours, can be represented by f(x + 20,…

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

Q: Using the figure below, where f' (3) = 2.1.f' (6) = 3.0,f' (9) = 3.7,f' (12) = 4.2, find (f-1)'(12).…

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Q: Differentiate. x2 -9 f(x) = In f'(x) = O

A: Explanation: Given that,  f(x)=lnx2-9x

Q: +4 2x. value Of X?

A:

Q: 3. y' = 3x? –2; y(1) = 5

A: When the linear differential equation is in the form, dydx+py=Q    ..........1 Then the solution of…

Q: x + + 8)(6y – 1) = 0 find the second derivative %3D

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Q: Solve X(Inx - Iny)dy - ydx = 0 %3D

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Find all complementary functions of the equation xy" - 2y'=0, x>0 1, x² x₁ x³ a. b. C. d. x, x(Inx)²…

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Q: what's y'' of y=4secx csc x

A: Given; y=4secx csc x

Q: Find y''' for y = 1/(x+4)3

A: To find the first derivative, y' of y, differentiate (x+4)-3 with respect to x, using the general…

Q: If f(x) = 3/7(2 – 7a + 5), find f'(x). - Find f'(3).

A: Given:- f(x) = 3√x(x3-7√x+5)  To find:- f'(x) and f'(3)

Q: x 3y'''- x 2y'' + 2xy' - 2y = x3

A:

Q: Explain what it means if a' . b = 0

A:

Q: 2. Find f'(x) for f(x) = x²e.

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Q: Find f. f ''(x) = −2 + 36x − 12x2,    f(0) = 5,    f '(0) = 18

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Q: Find f. f"(x) = -2 + 36x – 12x², (0) = 8, f'(0) = 18 "(x) =

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Q: f'(x) 6 48 3 8 Write down the value(s) of x for which the original function y = f(x) is a.…

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Q: (x*. In x dx = ?

A: Solution

Q: y= 30 Sqaure root x  y`(9)=?

A:

Q: One x value where f '(x) is negative.

A: fI(x) is the slope of the graph at any point . So, we will try to find the slope value at all points…

Q: 7 f(x) = 2x' + х— 2 + f'(x) = 2.

A:

Q: 24. (EXERCISE) Consider the function f(x)=3x* – 20x' + 42x² – 36x

A: The given function,   f(x)=3x4-20x3+42x2-36x

Q: 16xydx- 24ydy = -8x²dy %3D

A: The given differential equation can be written as:16xy−24yy' =−8x2y' An ODE Mx, y+Nx, yy'=0 is in…

Q: 19) Find f' if f(x)= sec² x 83√x

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Q: Solve X' ||

A: