12. Consider the function A(x) = sin(t2) dt. (a) Find A'(x) (b) Find the x-value of the first positive critical number of A(x) (c) At that first positive critical number you found in (b), does A(x) have a local max, a local min, or neither? Justify your answer

Q: Suppose you are given the derivative of some function p(t) as p '(t) = t.cos(10t) (a) Find the exact…

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Q: c. List any critical values. d. Identify intervals of increase. e. Identify intervals of decrease.

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Q: 2. Find the derivative of the following functions and write the down the inner and outer functions…

A: Solution: 2.(a) fx=2x5-4ex

Q: Let f(x) = (x³ +2x+4)* ƒ'(x) = = ƒ'(1) =

A: The function is f(x)=(x3+2x+4)4the aim is to find the derivative then the derivative of the function…

Q: Let f(z) ==+[=] Find f'(2). x+ [c]*

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: 1. Find the derivative f'(z) if it exists, and state where f(z) is analytic. *(i) ƒ(z) = (1 − 3z²)4.…

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Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

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Q: Where does the relative maximum value of f occur when f'(x) = x³ - x? (a). -1 (b). 0 (c). 1 (d). 2

A: concept first find x when f'( x ) = 0 if f''( x ) < 0 then maxima will occurs if f''( x ) > 0…

Q: 5. Use the given derivative to find all critical points of f and at each critical point determine…

A: Given that, f'(x)=4x3-9x

Q: 4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2…

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Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: Evaluate f'(x) at x =2 given f(x)= (x²– 3)“

A: The given function is fx=14x2-34. Evaluate the differential of function at x=2.

Q: 6. Find all critical numbers and use the Second Derivative Test to determine all local extrema. a)…

A: for part a see 2nd step. for part b see 3rd step.

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

A: Topic = Derivative

Q: (b) A "three-point formulas" for the derivative is 1 (-fo+ f2) 2h Apply it to f(x) = x' with xo,,x2…

A: The three point midpoint formula for  approximation error:                                     f1' ≈…

Q: 12 If f(t) = find f'(t). f'(t) =

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Q: 1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2