Problem 2.1 (max, argmax, min, argmin) Let f(x) := (2 + sin(2rx)) and A := [0, 2]. (a) Compute: max A f(x) and argmax f(x). XEA XEA (b) Compute: min,A f(x) and argmin f(x). XEA Compute: argmax |[2 ·e(x)+5 _ XEA -가. (c) (d) Compute: argmin [11 – In (2 · f(x) + 5)]. XEA

Q: If f(x) = (x + 1)²(x+2), find f'(0)

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Q: Simplify and find for each of the following functions without using product rule and dy dx DENT…

A: As per guidelines we are allowed to solve one question at a time so i am solving first one please…

Q: If f(x) = cos x + sin x, what is f"" (x)? 46 f""(x) = sinx- cos x f"" (x) = sin x + cos x o f(x) =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Step 4 To find (f-l)'(x) use the theorem that states that if f is differentiable on an interval I…

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Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

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Q: tan x If f(x) = 3 sec a f (2) = f (1) =

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Q: f(x) is a function such that f"(x) > 0 for x # 0 and f"(0) is undefined. Sketch 2 different graphs…

A: Here we need to plot two functions such that and f''(0) is undefined.In other words f(x) is concave…

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: Please help!

A: Recall the quotient rule for derivative:

Q: Suppose that cotx 3 find the value of cot (x − 3)

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Q: Suppose f and g are one-to-one functions such that f(2) = 7, f(4) = 2, and g(2) = 5. Find the value,…

A: We have given functions f and g are one-to-one. Then, a. gof-17=gf-17=g2=5 b. fog-15=fg-15=f2=7

Q: Composites of Functions

A: As per company guidelines, I can solve only first three subpart.

Q: is even, odd function or neither

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Q: For the function f, use composition of functions to show that f^-1 (the inverse) is as given

A: Given that: f(x)=x+63x-4

Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: 3 evaluate f sec³ (x) tan³(x)dx Select one: sec (x) sec (x) + C 3 sec (x) sec (x) + C 3 sec (x) sec…

A: Let's find integration of given function.

Q: 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +₁ Z-1 2) f(z) = 3z²…

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Q: Identify the original function f(x) and what value of c to evaluate f'(c). (3x-9x²)+(42) x+2 lim…

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Q: Let f(x) = In[x³(x + 6) 7 (x² + 5)³]. Find f'(x). 1 3 x²(x+6) ² (x² -5)³ f'(x) =

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Q: Plot the function f(x) = sin(x)cos(2x) and its derivative, both on the same plot, for 0<x<2n. Plot…

A: Given f(x) =sin2(x)cos(2x)⇒f'(x) =2sin(x)cos(x)cos(2x)-2sin2(x)sin(2x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.