Sketch the graph of a differentiable function y= f(x) through the point (4.4) if f'(4)=0 and satisfies the conditions given below. (a) f'(x) > 0 for x <4 and f'(x) < 0 for x>4 (b) 1'(x) <0 for x <4 and f'(x) > 0 for x>4 (c) f'(x) > 0 for x = 4 (d) f'(x) <0 for x #4 (a) Choose the correct graph below. OA. Ay Q 4 (b) Choose the correct graph below. OA. OB. OB. Ay 12+ H|||||| HIIH Q O C. O C. Ay 4- Q G OD. OD.

Q: F(x)= x-2 / x^3 F'(x)= 6-2x / x^4 F''(x)= 6x-24 / x^5  1. Find the local maximum and local…

A: To find local maximum and local minimum  and inflection points of given function.

Q: Given function f with f'(x)= 4-4x^2 / (x^2+1)^2 and f''(x)= 8x^3-24x / (x^2+1)^3 (a) Given the…

A: Given, f'(x) = 4-4x2(x2 +1)2  f''(x) = 8x3 -24x(x2+1)3 (a) If f is concave up then f''(x) &gt;0 So,…

Q: Domain: (-infinity,1) U (1,3) U (3, infinity) f'(x)>0 for (x 3). f''(x)>0 for (-2 3). f''(x)<0…

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Q: 4. The graph of a function f(x) is given below. 4. In the interval (-00, -3) a) f'(x)>0 and f"(x)>0…

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Q: Use the definition of a derivative to find f'(x) and f"(x). f(x) = 3x2 + 2x + 2 f'(x) = f"(x) =…

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Q: Use the definition of a derivative to find f (x) and f"(x). f(x) - 3x2 + 9x + 1 f(x) - F"(x) = Graph…

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Q: 14. Sketch the graph of f(x) which satisfies the following conditions: f'(1) = f'(-1) = 0, f'(x) 0…

A: Given conditions: i) f'(1)= f'(-1) = 0 ii) f'(x) &lt; 0, if |x| &lt; 1 iii) f'(x) &gt; 0 if 1 &lt;…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: 6. Sketch the graph of the function having the given characteristics. f(-6) = f(4) = 0 f'(-2) =…

A: Given the characteristics of the graph of a function:

Q: Use the definition of a derivative to find f'(x) and f"(x). f(x) = 4x² + 7x + 2 f'(x) f"(x)

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Q: Sketch a graph of f(x) satisfying all the following conditions: (1) f '(1) > 0 (2) ƒ "(1) 0

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Q: 1’) Let f be the function f(x) = x^2 +36/x^2 (a) Calculate f'(x) and find all stationary points for…

A: Solution - Given function - f(x)=x2+36x2 a.)        f'(x)=2x+36-2x-2+1             f'(x)=2x-72x…

Q: Consider the following. (The graph is called a serpentine.) (-4,-16) Find the derivative of the…

A: Given: The graph of the function fx=64xx2+64 and function passes through the point -4,-165 a) Find…

Q: Given the derivative f'(x), find the x-value for all relative extrema for the graph of the original…

A: Consider the given derivative. f'x=x2−5x+6 Put the first derivative equal to zero.…

Q: 3pts) Find the equation of the tangent line to the graph of the function f(x)=x-Vx at the point…

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Q: Select the true statements regarding a graph of f and its derivatives. □ If f'(c) · ƒ" (c) = 0, then…

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Q: The figure below shows the graph of f', the derivative of f, on the interval [-5, 4]. The function f…

A: The figure given shiws the graph of , the derivative of  on the interval .The function  is…

Q: [-4,0], the graph of f'(x)is a semicircle of radius 2 with minimum at (-2,0). [0, 0], f'(x) 2 – x.…

A: to find the inflection point we will see where the graph is changing its sign from increasing to…