The function f is defined by f (x) = x² – 2 – 5 sin (2x). Use a calculator to find all values of x on the interval -2, 2.5 such that the line tangent to the graph of f %3D has a slope equal to-4. Round your answers to the nearest thousandth.

Q: The derivative of the function f is defined by f' (x) = (x² + 4) cos (x - 3). If f(6) = -1, then use…

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Q: пу Show that if y = ax" where a is a real number and n E N, then dx where x + 0. 1 Given that f(x)…

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Q: Find the actual error when the first derivative of f (x) = sin(2x) at x = 1/8 is approximated by the…

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Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

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Q: For the given function, find the first derivative f' f(x) = e* · (3 sin x + cos x) + 4x3

A: Differentiate both sides of the equation, with respect to x using the product rule of derivative to…

Q: Find the actual error when the first derivative of f(x) the following 3-point formula sin(2x) at x =…

A: The actual value of the function can be calculated by calculating the derivative of the function.…

Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = n/8 is approximated by the…

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Q: 2. Find the derivative of the following functions: 5x + 6 (a) y = 8х — 1 )(",-) 2 8. - 8 (b) r =…

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Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 2. The height of a toy that moves up and down on a spring can be modeled by the function y = – cos x…

A: sin 2x =2sin x cos x

Q: Find d of the function given implicitly and evaluate the derivative at the given point. y = sin (…

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Q: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

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Q: Find the slope of the graph of the function at the given point.                         f(x) = 5 cos…

A: According to the question, we have to find the slope of function fx=5 cosx-9x at the point 0,5. The…

Q: Which of the following function has 10" derivative equal to zero? None of the given choices ®f(x)…

A: Explained below

Q: let f be a function whose derivative is given by f'(x)=( x/15) +sin(e^0.2x) . How many relative…

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Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

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Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

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Q: 6. Use the rules of differentiation to find the derivatives of the following functions. Do not…

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at x 1/8 is approximated by the…

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Q: The function f is defined by f(x) = x³ + 2 sin (2x + 3). Use a calculator to write the equation of…

A: From the given function; fx=x3+2sin2x+3 And x=0.5 Now find the y coordinate.…

Q: Find an equation of the tangent line to the graph of f at the point  (2, f(2)).   f(x) = 4(7x − 1)4

A: Given  f(x) = 4(7x − 1)4

Q: Find all values of x for the given function where the tangent line is horizontal.

A: Find all values of x for the given function where the tangent line is horizontal.

Q: Use the following derivative function f' to determine the local minima and maxima of the function f:…

A: Consider the provided question,

Q: Find the x-value(s) on the graph of the function at which the tangent line has the given slope. (a)…

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Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

A: Topic = Derivative

Q: find the function with the given derivative whosegraph passes through the point P.39. ƒ′(x) = 2x -…

A: We have to find the function for the given derivative passes through the point P: f'x=2x-1, P0, 0…

Q: The function f is defined by f(x) = x² + 2 cos (3x + 3x). What is the average rate of change of f'…

A: Average rate of change of a function f on [a,b] is given by f(b)-f(a)b-a. Computing f(10) and f(3).…

Q: Consider the following function. f(x) = x + 4x – 2, (1, 3) (a) Find an equation of the tangent line…

A: Given function is fx=x2+4x-2 and point is (1,3). Differentiating the given function with respect to…

Q: The function h is given by h(x) = cos(kx)ffx) for all real numbers, where k is a constant. Find…

A: The given function h(x)=coskxfx Differentiate with respect to x using the product rule…

Q: A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 – 2 (b). f(x) = 2 tan-1(x) –…

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Q: Find exact value(s) for x such that 3e" - e' = 0.

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Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: (4) Compute the derivatives of the following functions: (a) f(x) = 4x sin-1r

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Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

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Q: The derivative of y = 3 cos (V1-x²) + (1-x²) ² can be written as 3 1– x² sin ( V1-x²) - (1-x² ) 7 3x…

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Q: Consider the following. f(x) = x In xº, (-1, 0) (a) Find an equation of the tangent line to the…

A: We can use the application derivative in order to solve the given problem.

Q: A2) Find the derivative of the following functions: x² + 4 (a). f(x) x2 - 4 (b). f(x) = 2 tan-'(x) –…

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Q: Consider the function f(x) sin x +x. Using the following centered fifth-point formula of the first…

A: We have to use the given centered fifth point formula for the first derivative to find the…

Q: The function f is defined by f (x) = x2 + 2 cos (3x 2). Use a calculator to find all values of x on…

A: The given function is  f(x)= x2+2cos(3x-2) , x is in interval [-1,2.5]  Show that the line tangent…

Q: 2. a) Find f (x) if the function is f(x) = + sinx cosx b) What is the value of the derivative at? c)…

A: Given, f(x)= 1/sin(x) + 1/cos(x)

Q: (c) Use fzero to find when the derivative of 5. S(x) = 9. cos(x) sin(x) is 0 in the interval (0,…

A: NOTE: As per the guidelines we are supposed to answer only one question because all parts or…

Q: Find the actual error when the first derivative of f (x) = sin(2x) at x = 1/8 is approximated by the…

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Q: Find the actual error when the first derivative of f (x) = sin(2x) at x = 1/8 is approximated by the…

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Q: Consider the following. f(x) = x In x6, (-1, 0) (a) Find an equation of the tangent line to the…

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Q: Find the function f given that the slope of the tangent line to the graph of f at any point (x,…

A: Solution is done in step 2

Q: Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not…

A: f(x)=cosπx2

Q: take the derivative using the chain rule.

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Q: Answer the following questions for the function k(x) = x³ + x + 1: (a) The derivative at x = - is…

A: The given function is kx=x3+x+1