Example a. Find the values of x in the interval (-4, 4) at which g is not continuous b. Find the values of x in the interval (-4, 4) at which g is not differentiable. c. Sketch a graph of the derivative of g. y g(x) + + х -4 -3 -2 -1 2 3 4

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequ x2 + 1 an = n2.…

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Q: Use limits to find the derivative function ƒ′ for the followingfunctions f.b. Evaluate ƒ(a)for the…

A: a) Using the limit definition of f'(x) we get:

Q: Suppose that f(4) = 4, f’(4) = -2, g(4) = 5, and g’(4) = -3. Find the derivative of the function…

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Q: 14. The graph of f", the second derivative of f, is shown to the right for –2 < x < 4. What are the…

A: f will be concave down if f'' &lt; 0 . From the graph of f" we see that it is below the x -axis for…

Q: Draw a graph to match the description given. f(x) has a negative derivative over (- o, - 3) and…

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Q: Which is the most accurate table for the derivative function f'(x)? f'(x) f'(x) -3 -3 2.7 7 3 5.4 3…

A: we can solve  by discarded the option one by one

Q: Consider the following function. f(x) = x* - 16x + 72x? + 4 (a) Make a sign diagram for the first…

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Q: For the function y = h(x) whose graph is shown, find the values of x such that the derivative is…

A: For the given function: y=hx The graph shown is:

Q: The graph of function f(x) is shown below. At which value of a is the derivative of the function…

A: Explanation of the answer is as follows

Q: 2. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and…

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Q: If the derivative of f is given by f'(x) =e* - 3x , at which of the following values of x does f…

A: Topic- application of derivatives

Q: Consider the following graph of f'(x), the derivative of a function. f(x) 51 13 (a) State the…

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Q: Consider the following function. A(x) = |7 – 8x| Find the derivative of the function. if x Find the…

A: Given, A(x)=7-8x ⇒A(x)=7-8x, x&lt;788x-7, x&gt;78

Q: Let (x0, yo) = (2,6) and (x1, Y1) = (2.5, 6.2). Use the following graph of the function f to find…

A: Given that, The points of passing of function f are following, (x0, y0) = (2, 6)   and     (x1, y1)…

Q: Which is the most accurate table for the derivative function `f'(x)? f'(x) 'f'(x)` f'(x) f'(x) -3 -3…

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Q: The figure above shows the graph of f, the derivative of function f, for -6 < x < 8 . Of the…

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Q: Find the derivative of the function at the given point in the direction of A. f(xу,2) - 4x - 5у -…

A: Use the formula of the directional derivative and solve accordingly.

Q: Suppose the derivative of the function y = f(x) is y' = (x- 4) (x- 3). At what points, if any, does…

A: First we find out critical points putting y"=0 then find out 2nd derivative test .

Q: Suppose L is a function such that L'(x) = 1/x for x > 0. Find an expression for the derivative of…

A: Given:- Suppose I is a function such that L'(x) = 1/x for x &gt; 0. To find:- An expression for the…

Q: The graph of function f(x) is shown below. At which value of z is the derivative of the function…

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Q: Suppose L is a function such that L′(x)=1/x  for x>0. Find an expression for the derivative of each…

A: Given: L'(x)=1x       for x&gt;0…

Q: 2. The graph of f is shown in the figure. Sketch a graph of the derivative of f. y 8 10. 6 4 2 - 6…

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Q: Let (x0,y0)=(2,6) and (x1,y1)= (2.5,6.2). Use the following graph of the function f to find the…

A: We first find the slope of f(x) at x=2 using the given tangent. Slope=f'(2)= slope between (2,6) and…

Q: 25. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and…

A: For the given graph of the derivative of f(x) . We have to find out which of the following is…

Q: 5. (Refer to the graph of f below) For what value of x is the derivative off equal to zero? 2 -4 -3…

A: Consider the graph

Q: For the function f graphed below, sketch a possible graph of its derivative f'. y 3.0 2.5 2.0 1.5…

A: The derivative of a function means the magnitude of the slope of the tangent to the curve. The graph…

Q: A. Find the derivatives of the following functions: W 1. f(x) = (-x* - 5) 2. f(x) = (-x- 4)-2 %3D

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Q: Let `h (x) = -3tan^5(-7x)` Determine the derivative of 'h`. (I 'h'(x)=' Determine the slope of `h`…

A: We have to find h'(x) and h'(7)

Q: Let g be a function with derivative given by x2 - 2x - 8 g'(x) = V2x³ +5 - 1<x <5 %3D . At which…

A: Occours

Q: Let (x0,y0)=(2,6) and (x1,y1)= (2.5,6.2). Use the following graph of the function f to find the…

A: Given points that lie on tangent are:

Q: Use the first, and second, derivative (given below) to find the intervals of increase/decrease and…

A: Follow step 2 and 3 .

Q: A.1 relative minimum, 1 relative maximum, and 3 points of inflection B.1 relative minimum, 1…

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Q: The figure above shows the graph of f′ , the derivative of function f, for −6<x<8 . Of the…

A: Given query is to find the correct option which discribe graph of f(x).

Q: The graph of a function, h(x) is shown to the right. Which of the following conclusions can be made…

A: Given

Q: The graph of f’, the derivative of the function f, is shown above. If f(0) = 0, which of the…

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Q: The limit below represents the derivative of some function f(x) at some number a. 5(2 + h) – 160 lim…

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Q: Assume that functions f and g are differentiable with f(- 3) = – 5, f'(- 3) = – 5, g(-3) = 4, and…

A: Given F(x)=f(x)g(x)

Q: (a) Consider the following graph of a function y = f(x): -2 (i) Sketch the graph of the derivative…

A: The graph of the function f(x). We have to find the graph derivative f'(x).

Q: 1. For the function h(x) whose graph is shown, find the values of x such that the derivative is…

A: (a)Given that,h'(x) &gt; 0Here, derivative is positive.When derivative is positive , the function is…

Q: 2) Consider the function defined by g(x) = 5x - 4. You may use the graph of this function to…

A: Recall: Derivative(|x|)=xx

Q: Suppose the derivative of a function f is given below. On what interval is f increasing? (Enter the…

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Q: Consider the following function. f(x) = x?(x - 8) (a) Make a sign diagram for the first derivative.…

A: Answer A:

Q: If f(x) = 4x2 – x³, find f'(x), f"(x), f'(x), and f(4)(x). f'(x) = f"(x) = f""(x) = f(4) (x) = Graph…

A: Given, the function f(x) = 4x2 – x3, then we have to find the f’(x), f’’(x), f’’’(x) and f4(x) and…

Q: Consider the following function. p - 5 h(p) = p2 + 9 Find the derivative of the function. h'(p) =…

A: Given function is: h(p)=p-5p2+9 To find the derivative of the function h'(p) Use quotient formula of…

Q: 6. let h be the function defines by h(x) = 2e*+tdt, Find h'(2) 7. let g be a function whose…

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Q: Which of the following statements is TRUE? a. If f '(3) = 5 and g '(3) = 4, then the graph of f (x)…

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Q: Suppose f(x) = x^3 . Using the definition of derivative, compute both f'(x) and f''(x). (Hint: You…

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Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: 5. a) Identify f, f', and f' from the graph below. b) Sketch the graph of the derivative in the…

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Q: 6. (Refer to the graph of f below) This derivative value is the least among the given. 2 1 -4 -3 -2…

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