1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x < 0 ax² + bx + c; 0 < x < 2 f(x) = -ax² + 1 + 5; x > 2 4

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: A curve, y=f(x) passes through the point (1, −1)(1, −1) and the slope of the tangent at any x is…

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Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

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Q: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

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Q: if f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1, then the derivative of f(x).g(x) evaluated at x =…

A: Given: f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1

Q: 2. Find the derivative of the following functions: (5x+ 1)'(x + 3)5 cos°(x) sin°(x) (a.) f(x) = .…

A: Given f(x)=5x+77x2+35cos2x sin3x3   As per our guidelines we are supposed to answer only first…

Q: 01) Find the derivative of the following: x2 + 3 y (x – 1)3 + (x + 1)³ 2x2 + tan x f(x) : %3D x2 sec…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivatives of the functions g(x) = tan 3x/(x + 7)4

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Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: Find f'(1) of f(x) = x3+ x and use it to find an equation of the tangent line to the curve above at…

A: f(x)=x3+x Slope of a tangent to a function f(x) at point x=a is defined as the value of f'(a).…

Q: The derivative of f(x) = 2 cos 2x is an odd function.

A: Odd function

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

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Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: f. y=In(x8+1)

A: We will solve the problem

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

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Q: 5. Find the requested derivative for each function, and simplify (reasonably): a) f"(x) for f(x) =…

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Q: Consider the function g(x) whose derivative is given by g'(x)=-(2x-3)sin(x²-3x).At which of the…

A: To find the relative minimum, first find the critical point by equation g'(x) to zero and solve for…

Q: 59. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

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Q: Suppose that functions f and g and their derivatives with respect to x have the following values at…

A: Note: Since we are authorized to answer three sub-parts of a question at a time. And you have asked…

Q: Which of the following function has 10" derivative equal to zero? A f(x) =(3x²-4x +2)³ B f(x)…

A: Here we find out whic function 10th derivatives is zero.

Q: 6.) Find the derivative of the following functions a.) f(x)=- 7-3х |t +1 b.) f(x)=. -1 c.) f(x)= ean…

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: A function, f, and its derivative are given below. Which of the following is an equation of the…

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Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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Q: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

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Q: 2. Find the derivative of the following functions: -2 (a). f(x) = x² + 4x + 4e" (b). f(x) = 2…

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Q: 11. (a) Find F'(x) using the limit definition of the derivative if F(x) = F'(x) will result in zero…

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Q: Find the natural domain and the derivative of the given function. (a) ln(4x + 2) (b) x · cos x (c)…

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Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: The derivative of the function f is given by ƒ'(x): = e¯* cos(x²), for all real numbers x. What is…

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Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…