Find all relative extrema of the function. Use the Second Derivative Test where applicable h(t) = t − 4√(t + 1)

Q: 7. Use the definition of the derivative (long method/ increment method) to find the derivative of…

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Q: Given f(x)= (x^2)/(x^2-4) a) Find the derivative b) Find the critical points

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Q: find the first derivative of the function: F(x)= (1+t^2)^-3 (t-1/square root t)^4

A: From the given problem:   ft=1+t2-3t-1t4   From the product rule:   f·g'=f'·g+f·g'   So,…

Q: Find the (a) true error and (b) relative error of the following: The derivative of f(x) = 2−x at x…

A: For the solution follow the next step.

Q: Find the derivative of the function below. (Do not simplify your answers, and SHOW ALL STEPS) f(x) =…

A: Use the concept of derivative of the form f(x) = uv

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Use the derivative of the function shown below to determine the open intervals in which the function…

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Q: What is the derivative of f(x) = Select the correct answer below: O 4V/2 O 2012 3 O w/s O 16V/2 о 3…

A: Derivative of function f(x)=43x54 at x=4

Q: Q2/ A) Use the definition of the derivative to find f(x) where f(x)=v3x+1

A: To find the derivative of given f(x) using the definition of the derivative.

Q: Fi ind the derivative with respect to x of f(x) = ( (3x³ + 8)' + 4) 9 + 2.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 2. If u3 = a³t, find· d?u where a is a constant. dt2

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Q: Q2. Use the definition of the derivative to find ý of the function y = sin(x). %3D

A: Here given function is  y = sin(x)

Q: b) f(x) = xe

A: If f(x) is a function of x and the second derivative of f(x) exist at any stationary point x0.1.If…

Q: f(x,y) = 2y3–3y² – 12y+2x2 – 4x+2.

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Q: A derivative formula

A: dax+bdx By using the definition of derivative, we get…

Q: Using the definition, find the derivative of f(z) = 3 z4-6 z at point z= 0

A: The derivative of the function f(x) is given by f'x=limh→0fx+h-fxh. The given function is…

Q: Use the definition of the derivative (long method/ increment method) to find the derivative of the…

A: We will find the derivatives.

Q: Find the derivative of the function. z(=) = v + 5 7

A: d/dx (xn ) = n.x(n-1)

Q: Write down the solution and Choose the correct answer Q1) The dervative of the function f(x)= x+2…

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: derivative

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Q: Vhat is the second derivative of f(x) = x'e? II

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Q: Consider the function x + 3 f(x) = + V9+ 3x 6 – x Use the definition of derivative to find f'(0).

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Q: Find the derivative of the function. f(t) = arccsc(-3t2) 1 f'(t) = |-37|V94

A: Given,To find derivative of F(t) = arccsc(-3t2)

Q: Find the derivative of the function f(x) = V (2² – 2)° 2 at x = 1. f'(1) = Preview

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Q: 3. Use the formula ((x+h)-f(x) to approximate the derivative of f(x) = 3x² at x = 1 h using h = 0.1.…

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Q: (a) Use the definition of the derivative to calculate the first derivative f'(x) for the function…

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Q: Find the derivative. Then evaluate at x = 0 f(x)=√(2x+9)3   The answer is f(x)'= 3√(2x+9)   ;…

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Q: Find the derivative of the given functions: 2. f(x) = rcos(rx) – 6 sec(x) + 3

A: Given that, f(x)=rcos(rx)-6secx+3When r=4we have,f(x)=4cos(4x)-6secx+3

Q: Find the derivative of the function g(x)=x2∫0√1+t2dt.

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Q: Find the absolute extrema of the function f(x) = (x2 + 18)273 on the interval[-4,3]. Find the second…

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Q: Given the function y = f(x) = /x² + 1 a. Use the first derivative to find the intervals

A: The function is given y=fx=x2+1. a To find increasing or decreasing function. y=x2+1 Take the first…

Q: By the first principle (The definition of Derivative) to find the derivative of f(r) V3r + 1. %3D

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

Q: Find the derivative of the function. 14) f(t) = (3 - t)(3 +3)-1 %3D

A: Given the function f(t)=(3−t)(3+t3)−1

Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A: Given function is fx=x44-5x33-4x2+48x. For critical points we need to find first derivative of…

Q: Calculate the derivative of the function. f(x) = V 9x + x2 t'(x) (No Response) Need Help? Read It

A: Given: f(x) = 9x+x2 To find: The derivative f'(x) of the given function.

Q: 4 Find the derivative of the function f(x) = %3D x +7 Provide your answer below: f'(x) =

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

Q: t(x)=23x3−10x2+42x+9 Given the function above, use the First Derivative Test to find the local…

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Q: Find the derivative of the function. h(s) = -2/ 9s² + 2 %3D h'(s) = %3D

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Q: a) Determine the derivative, y (x) for the composite function below. g(x) ]V y(x) =

A: Equation of normal line

Q: 2the second derivative test to find the loscal maxilnum and minimulin of thie functioni 3 f (x}こ 2メ2…

A: To find the local maxima and local minima of the below function. fx=2x3−3x2−12x

Q: Find the derivative of the function. f(t)=(1+sqaure root of t)(2t^2-3)

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Q: Find the derivative of the function. V5 -4 f(s) = Vs +2 Choose the correct answer below.

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Q: Find any relative extrema. Where applicable, use the Second Derivative Test to verify. (a) f(x) = (x…

A: a)  f(x)= (x+9)2 b)   f(x)= x4 -2x2 +6 c)  f(x) = 2x +18/x          provided x≠0 To find relative…

Q: Find the derivative of the function. F(t) = etsin(2t) F'(t) =

A: We can find the derivative as below.

Q: Find the derivative of the function 4/ f f(x) = V (x – 3) at x = 2. f'(2) =

A: fx=x2-354⇒fx=x2-354 Differentiating with respect to x, we get f'x=ddxx2-354=54x2-354-1·dx2-3dx…

Q: Find the derivative of the function. f(x) = /7+ V5+ VI f '(x) = %3D

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: C45 O Use the first derivative test to find the local extrema of f(x) where f(x) = 4x3 - 36x.

A: (A)- local maximum at - root(3) and minimum at root(3)

Q: Using the definition, find the derivative of f(z) = 3 zª-6 z² at point z= 0

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