The table below shows values for four differentiable functions. Suppose we know the following things: t'(x) = g(x) g'(x) = h(1) h'(x) = f(x) f'(x) = t(1) 0 1 2 3 4 h(z) 13204 t(z) 21430 g(x) 34 102 f(1) 0 2 14 3 What is 5[*h(z)dz? What is is [* (t(z). (t(x) + 4)dx? What is the equation of the tangent line to the curve y = f(x) when I = 2? Answer: y =

Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) =…

A: We have to find the solution of differential equation.

Q: If ƒ(x) ƒ'(x) = - 53 x - 7' what's f'(x)?

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Q: 2-45+1 if エ-1

A: Given function is: fx=3x2-4x+1x-1 ; if x≠12  ;  if x=1 Then we get, for x≠1:…

Q: Given the graph of the function f below. Which of the following has the highest value? f'(-2) f' (})…

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Q: - For the following graphical representation of a function f(x): (1) Mark the points on the graph…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: 2. Given the following graphs of the first and the second derivatives of the function f(x) and the…

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Q: Find the second derivative. 9. f(x) = V4x-5 f"(x) = f'"(x)=|

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Q: A motorcycle shop estimates that it will sell 600 motorbikes in a year. Each bike costs $250, plus a…

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Q: ider the graph of the function f(x) = x¹. n change in the function rule will translate f(x) to the…

A: Given query is to find the option which translates the function in left.

Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: h' (2) = 4, then f'(2) = ? We know the following 5. Suppose that f(h) and h(r) are functions such…

A: Using the given value we find the composition function value and value of f’(2)

Q: Using the definition of the derivative, compute f'(x) for the following functions. (a) f(r) = -3 (b)…

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Q: Use the table below to find h'(-1) for h (x) = f (g (x)). I()9() lO() 1/2 0. -2 -3 1. -1 -1 -2 -2 -2…

A: Given that hx =fgxTo find : h'-1Solution hx =fgxh'x =f'gx×g'xx=-1h'-1 =f'g-1×g'-1h'-1 =f'-2×2h'-1…

Q: Given functions f and g for which f(- 6) = 1, ƒ'( – 6) = 1, g( – 6) = 6, and g'(- 6) = 2. Evaluate…

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Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: 2. (a) Sketch the graph of y = f'(x) given the graph of y = f(x). (b) Specify the domain and range…

A: Graph

Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: 4 Find the derivative of y = 8* +

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Q: 2. For the function, f(x), below, state the intervals of increase and decrease, the x-coordinates of…

A: The interval of increase: From the graph of the function, we can see that the function is increasing…

Q: ļim (* +4)- ƒ(x) 3. Find the derivative of the following functions using the Show all your steps. a.…

A: f'(x)=lim(h tends to 0) {f(x+h)-f(x)}/h use this for derivative