I. Given f do the following: A. Find all possible points of inflection of the graph of f in I. Identify the subintervals of I where the graph of f is concave up or concave down. B. Find all critical numbers of f. Use the Second Derivative Test (SDT) to determine if the critical number is a relative maximum point or relative minimum point or if SDT does not provide a conclusion. 1. f(x) = cosh(3x – 2)

Q: Find the critical points of the following function. Assume a is a nonzero constant.

A: Critical points are the points where the first derivative is zero or not defined. So differentiating…

Q: 5. Find the critical points of the following function, and classify the critical points using the…

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Q: Find the critical points of the following function. 1 Inx f(x) =

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Q: Find the critical points of the following functions. Assume a is a nonzero constant. f(«) =

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Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

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Q: Find the critical points of the following function. Assume a is a nonzero constant. ƒ(x) = x3 - 4a2…

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Q: Provide what is asked for in each item. 23 with f'(x) = 3a (9 – a²) (9 – 3x2)2 54.x(x² + 9) (9 –…

A: Given problem:-     d. Make a table that shows the intervals where f is increasing or decreasing,…

Q: Say whether the following is true or false: If c is a critical point of f , then f has a local…

A: If c is a critical point on f then the point c could represent a local minima, a local maxima or a…

Q: : Find the critical Points of the following function fw = Sinx - Sinx- I OS XS2 7T |

A: Given function is: fx=sin2x-sinx-1   , 0≤x≤2π

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Q: Suppose that the first derivative of f(x) = is approximated by the following formula %3D 3x+4 -2f(x…

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Q: Answer the following questions on . f(x)=x^2(third root  of (x-7)) (a) List all critical values of…

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Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Given: And

Q: Use the graphs of f(x) and g'(r) to answer the following 5 problems. 1.) Find the absolute extremes…

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Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: f/x=x-12x+2 a). Critical points are the values of x for which first derivative is zero or not…

Q: Find the critical points of the following function. Assume a is a nonzero constant. ƒ(x) = 12x5 -…

A: The given function is fx=12x5-20x3. In order to compute the critical points, solve the equation…

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

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Q: Given f(x) = In(x² + 3x + 9), over the interval [ – 5, - 1], answer the following: %3D a) The point…

A: Given,           fx=lnx2+3x+9

Q: If f"(c)<0, where c is a critical value and f(x) is a continuous function over an open interval I…

A: We have to find f(c)

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Given f'x=(x-2)(x+4)(x+1)(x-3),x≠-1,3 (a) To find the critical points of f. (b) To find the open…

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Maxima minima: ƒ'(x) = (x - 7)(x + 1)(x + 5) Critical points of f exist in those points where…

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) &gt;0. Does f have a local…

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Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

A: Consider the given data,f'(x)=4-5xx+93and f is continuous everywhere

Q: If f"(c)<0, where c is a critical value and f(x) is a continuous function over an open interval I…

A: The answer is that f ''(c) tells us the concavity of f(x) at x = c. If f(x) is concave up, i.e., if…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the calue of c…

A: Given function is

Q: C are the critical values and the function is not defined at B. following intervals, tell whether…

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Q: Given f(4)=5.671,f'(4)=12.325, f" (4)=21.01,f"'(4)35.789, f''(4)=43.072 that all other high order…

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Q: 5. Ifc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

A: To give the condition of local maximum or minimum at c if c is a critical point of F(x).

Q: ind the minimum and maximum values of the function on the given interval by comparing values at the…

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Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: Find the critical points of the following function. Assume a is a nonzero constant.

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Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Given: f'x=x-1e-x we know that critical points are define as points on graph of a function where f'x…

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Use the Second Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: Find the critical points of the following function. Assume a is a nonzero constant.

A: Given: fx=xx-a To determine: The critical points of the given function.

Q: Let C be a real number and let f(x) = . If the slope of the tangent line to the graph of f(x) at its…

A: fx=Cx33-9Cx22 Differentiating with respect to x, we get f'x=C3·3x2-9C2·2x=Cx2-9Cx Again…

Q: Consider f(x) = xlnx on the interval [1,6]. When will the first derivative equal zero? For each…

A: Given that: f(x) = xlnx   x∈[1,6] To find: When will the first derivative  equal to zero. And for…

Q: Answer the following questions on f(x)=x²(x-7). (a) List all critical values of f from the smallest…

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Q: Find the critical points of the following function. Assume a is a nonzero constant.

A: Given: fx=4x55-3x3+5.

Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Let f(x)=x3−3x2−9x+25. Use the derivative f′(x)=3x2−6x−9 to determine the following values for f on…

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Q: Answer the following questions on flx)=x²(Jx-7). (a) List all critical values of f from the smallest…

A: When f'&gt;0 then function increasing when sign of f' changes from negative to positive then that…

Q: The graph of f"(x), the second derivative of f, is shown below. If the point (4, f(4)) is a critical…

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Q: Find the critical points of the following function f(x)=|x-1|+|x-2|

A: Given:                      f(x)=|x-1|+|x-2|   To determine:                               Critical…

Q: Let C be a real number and let f(z) = If the slope of the tangent line to the graph of f(x) at its…

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