I have a question about part(b). I know that F(x)=P(X < x) = integrate of f(t)dt. It is easy for me to get F(x) when -1

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 f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f'(1). f'(1) = -16/17

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Q: 2 Let f(x) = √3x² + 3x + 2 f'(x) = ƒ'(1): = OF

A: Topic - Derivative of  a function We are given, f(x)=3x2+3x+2Formulas usedChain rule:…

Q: (a) h(x) = x^√√x² +1 (b) f(x) = (3x² - 2x+1)³(x¹ -2r²- 3)² 4 (c) g(x) = (3-4) ¹ 5x+7

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Q: If f(x) x = √₁² (2²³ + Sº (t³ + 5t² + 2), dt then ƒ''(x) = =

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Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

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Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

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Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

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Q: Let f(x) = √√4x² 4x² + 3x + 5

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Q: f f(x)=- X+1 2x+1 1 = (2x + 1)²* 1 (2x + 1)² O 3x+1 (2x+1)²* 3x+1 O (2x + 1)² then f'(x) =

A: Topic: derivatives

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

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Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

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Q: Find a function f(x) such that ƒ'(x) f(x) = – 6x² – 1 and ƒ(0) = 5

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Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = -2x³ f(x)=

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Q: Explain why f(x + h) – f(x - h) 2h should give a reasonable approximation of f'(x) when f'(x) exists…

A: Explain why fx+h-fx-h2h should give a reasonable approximation of f'(x) when f'(x) exists and h is…

Q: Suppose that f(x) 2 4x Find f'(x).

A: use quotient rule for differentiation

Q: Given f()= 2x + 1 and ()= r*+ 2x-1, fnd (f- (1).Then valute the difence when x=2.

A: Sum and difference of the two functions

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Let 1 + 1 f(x) = 9x - 2/x + 4x + %3D Find f' (1). Enter your answer as an INTEGER: f'(1) =

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Q: can i get help step by step

A: We have to essentially find the integral of the given function

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: If f(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

Q: if f(x) = 3x+4 over 4x+3 then f'(x)=?

A: Given: fx=3x+44x+3 To Find: f'x=?

Q: Compute the derivative of f(x) = (x² + 3)e7x+5. O (x² +2x+3)e7x+5 O 14xe7x+5 O (7x2 + 14x + 21) e7+5…

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Q: Let F(x) = f(f(xæ)) and G(x) = (F(x))² . You also know that f(9) = 3, f(3) = 2, f'(3) = 5, f'(9) =…

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Q: Let f(x) = ƒ' (5) = f" (5) = f"" (5) = 1-4x 1+4x Compute the following.

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Q: x²-1 3. f(x) = -1;ƒ' (1) 2x+1

A: Solution is given below:

Q: Can i get help step by step

A: Derivative is given. We have to integrate the same to obtain the original function and then apply…