Find the two x-intercepts of f(x) = x2 − 3x + 2 and show that f′(x) = 0 at some point between the two x-intercepts.

Q: Find the indicated derivative of the function. 1) d'y of y - 6x5 - 4x2 - 4x + 1 dx4

A: According to bartleby guidelines I have to solve only one question.

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: Find the first and second derivatives of the function. x2 f(x) 7 + 8x f'(x) %D f"(x)

A: Use the concept of derivative of the form y = v/u

Q: f(x) = −x2 + 6x − 12 y-intercept(x, y)=

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Q: Find the second derivative of the function f(x) = 2 – 3x + 5æ/2 – 7e" . 15 f"(x) = –3+ 2 7e" f" (x)…

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Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…

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Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

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Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

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Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: find the point at which the line g(x)=−1x+0g(x)=-1x+0 intersects the line k(x)=−4x+9

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Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Determine the values of constants a and b so that f(x) = ax^2 + bx has an absolute maximum at the…

A: Given that  f(x) = ax2 + bx has an absolute maximum at the point (1,2).

Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

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Q: Find the derivatives of the functions in Exercise

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Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

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Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and…

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

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Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: Find the derivatives of the functions y = (x2 - 2x + 2)e5x/2

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Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

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Q: find the homogenous linear equation of the function y = x2 sinx+ e5x

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Q: 3. Find the second derivative of f(x) = 2sin²(3x) а. 36сos? (3x) — 36sin? (3x) b. 36сos (3x) —…

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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Q: Find the particular solution determined by the initial condition. f'(x) = rx) = 2x2/5 - 3x, f(1) =…

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Q: Determine the values of x at the critical points of f(x)=x -3x -0.25x+3.75 and classify each…

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Q: Find all the higher derivatives of the function f(x) = (4x-5)°. P (x) =] f"(x) = f"(x)=

A: Differentiate above function with respect to x

Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: Find the solution of y-x =0 using separable variable method. dx

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Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: For the function f (x) =x³ – 3 -x² + 8 , find the coordinates of all Critical Points.

A: Given, fx=x3-3x2+8

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

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Q: Use the intermediate value theorem to show that the equation x^3+x^2−2x+1=0 has a solution i the…

A: (note - I assume i as iota) f(x) = x3+x2-2x+1 At x= -1,      f(-1) = (-1)3+(-1)2 -2(-1) +1…