Solve the following problem when y(0) = y'(0) = 0. (20t 0≤t<5 t≥ 5 y" + 16y = f(t) = {20t

Q: Differentiate. ax + b f(x) %3D Cx + d f '(x) =

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Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx &gt; 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: If h(x) = √6 +5f(x), where f(3) = 6 and f '(3) = 3, find h'(3).

A: To find the derivative of given function

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Q: Find f. f"(x)  =2/3x2/3

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Q: If 69 + 5 f(x) + 2x²(f(x))³ = 0 and f(1) = -3, find f'(1). f'(1) =

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Q: If f'(x)=8x' – 6x² +10x – 9 and f (1)=24, find f(x).

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Q: If 4 – x2 f(x): 2 + x2 find f' (x). f' (x) =

A: Given function is Differentiating both sides with respect to x by using quotient rule of…

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: If f and g are functions that satisfy f'(2) = -3 and g'(2) = -1, find h'(2) for h(x) = -5f(x) +…

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Q: Find f. f"(x) = -2 + 18x – 12x2, f(0) = 3, f'(0) = 14 f(x) = %D

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Q: Find f. f(x) = f"(x) = -2 + 18x - 12x², f(0) = 3, f'(0) = 12

A: Integration

Q: 2x-3 3x (x-3)2 find the x-value(s) where k'(x) is (are) undefined. If k' (x) : for all x in the…

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Q: function of xx if

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Q: Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct…

A: f(x)= (0.2x+2)(0.6x-9)

Q: Find f. f"(x) = -2 + 30x – 12x2, f(0) = 8, f'(0) = 16

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Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

Q: If h(2) 9 and h'(2) = -4, find %3D %3D d (h(x) dx x = 2

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Suppose f(x) = (x² + 1) · g(x), where g(æ) = mx + b. Find the slope, m, of g if f(0) = 3 and f' (1)…

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Q: Find f. f"(x)  =20x 3    +12 x2    + 4  ,    f(0) =8,  f(1)  =5

A: Given, f''x=20x3+12x2+4f0=8, f1=5

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

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Q: h(x)=px^(3)+4px+(q)/(x), where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: The objective of the question is to find the values of the constants p and q in the function h(x) =…

Q: 3. If f'(x)= 3x² 2 and f(1) = 4, find f(e).

A: To find f(x) from f'(x) we integrate it C=integrating constant

Q: Suppose H(x) = f(g(x)) and %3D f(14) = 3 f' (2) = 13 g(14) = 2 d (14) = 4 Find H' (14)

A: Chain rule of differentiation:

Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…

Q: Determine h' (x) when it is given that [h(2x)] 16

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Q: If f(1) = 5 and f'(x) > 2 for 1< x < 6, then the smallest value of f(6) would be

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