3. Consider the function A(x) = f cost sin³ tdt for x in [0, 2π]. Calculate A'(x), determine the intervals of increase/decrease and the critical points of A on (0, 27), if they exist. • Compute A(). • Sketch the graph of A on [0, 2π] using the above computation and the following information: A"(x) < 0 if and only if x in [0, ) U (2, 4) U (5,2π].

Q: 3. Sketch the graph of a function that satisfies all of the given conditions. • f'(0) = f'(2) = 0 •…

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Find f(x) if f(4) = -8 and the tangent line at (x , f(x)) has slope 7o* + 4. O a. f(x)= 7e* + 4x –…

A:

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

A:

Q: Let f(x) = 0 for x < 0 and f(x) =x3 for x ≥ 0. Match the following. Here DNE means does not exist.…

A: Givenf(x)=0,x&lt;0f(x)=x3,x≥0We need to findf'(0),f''(0),f'''(0)

Q: 4. Let f(x) = e3h(x) and g(x) = h(e3"). Find f'(7) and g'(2) given that h(7) = 2, h'(7) = 4, h'(e) =…

A: We have to find

Q: \lim_(x->\infty )(e^(-x)+2cos 3x)

A: See the answer below

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

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A:

Q: Given f''(x) = 8x + 6 and f'(0) = 1 and f(0) = 2. Find f'(x) =

A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

Q: 11 Find /(x) if ƒ (1) = and the tangent line at (x, f (x)) has the slope 1 1xe*²-1 1 Oa. O b. 1le*-1…

A: Using formula of slope of tangent &amp; integration to find f(x)

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: 4. For the function f(x) = x³ – 3x? (-1<x<3) (a) Find f' and f". (b) Find the critical points. Which…

A:

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

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A:

Q: Suppose that g is a function that is differentiable at x = 8 and that g(8) = -4 and g' (8) = 3. Find…

A: Given,            Suppose that g is a function that is differentiable at x=8 and that g8=-4…

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A:

Q: Suppose we have two interesting functions f and g. We have limited knowledge of them as follows: •…

A:

Q: 10. Use the given information to find f"(2) of the function f(x)=g(x)h(x). g(2)= 3 and g'(2)…

A:

Q: ) Given the function f(x) derivative f"(1) with h, h/2 and h/4. 5. e Vx cos (Tx), approximate the…

A: Given function is  For this answer, we choose  We have  (up to 4 decimal place accuracy) We also…

Q: Given f'(x)= Ox=8 Ox=4 Ox=2 Ox=0 x²-8x (x-4)² determine the x-value where a relative maximum exists…

A: Given , to determine the x-value where  a relative maximum exists  for .