Let F(t)= (cost)i + (sin)j. (a) Show that + F = 0 (b) Show that there is no value of t on the range 0

Q: Given the function below f(x) = 3 x³ – ²x² − 18 x + 3 a) Differentiate the functionƒ(x) = 3 x³ − 2…

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Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

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Q: Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point…

A: Consider the conditions for the mean value theorem.

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

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Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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Q: for function f(x) = e=z²/(20²) sketch f(x)!

A: Topic :- Calculus

Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Let f be the function given by f (x) = 3*. For what value of x is the slope of the tangent line to…

A: Given, fx = 3x  We have to find the value of x at which the slope of the tangent line to the curve…

Q: Identify the plot below that represents a function f(x) that satisfies the following conditions:…

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Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

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Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

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Q: find a function f for x>0 so that f(x,y)=yf(x)+yf(x)

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Q: 6. FinD F(S) if f(t)= t· cost

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Q: Let / be a differentiable function that satisfies Then f(x+y)-f(x) = 6 xy + 3y2 for any real numbers…

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Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: For f(z) = 2es'the value oflog(f(z)) is

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Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

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Q: If f(x) = 7x5 - 6e", find: ƒ'(x) = ƒ' (1) = ƒ''(x) = ƒ'' (1) =

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Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

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