Find all the value(s) of z at which(x)3z2 -z+9 has a horizontal tangent line.If there is more than one 3,5. answer, give all of the z-values separated by commas, e.g. if f(z) has a horizontal tangent line at z3andz 5enter +3z 9 has a horizontal tangent line. If there is more than one Provide your answer below:

Q: Find all the value(s) of x at which f(x)=4x33−7x22−15x+10 has a horizontal tangent line. If there is…

A: Given the curve y=f(x)=4x^3-7x^2-15x+10. To determine at what points the tangent is parallel to the…

Q: Determine the zeros (x-intercepts) of the following function. Why can Rolle’s Theorem by applied to…

A: 3x^2-15x-18 3x^2-18x+3x-18 3x(x-6)-3(x-6) (x-6)(3x-3)   Zeros = 1,6

Q: Find any critical numbers for ƒ and then use the second derivative test to decide whether the…

A: Given, ƒ(x) = x2 - 12x + 36 To find critical points of the above function and find the relative…

Q: The function f has a continuous second derivative, and it satisfies f(7)=5, f′(7)=4 and f″(7)=−2. We…

A: f"(7)=-2 Since f " (7) < 0 so at x=7 f(x) is concave down.

Q: 5. Find the length of the curve f(x) = x², on [-1, 1]. %3D

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Q: Consider the function f(x)=x3−3x on the closed interval [2,4]. Find the exact value of the slope of…

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Q: 1 is discontinuous. Find the distance between the two values of x at which the function x² -3x + 2

A: Given rational function is as below

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A:

Q: The function f(x) = 13x – In(7x + 14) has a single critical number at x = A. Find this critical…

A: To find the critical number of the function

Q: The inflection point for y in the interval [0,15] is located at (give both coordinates!):

A:

Q: Consider the function f(x) = 2x – 5x on the closed interval [- 3, – 1]. Find the exact value of the…

A: Explanation of the answer is as follows

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4e* on the interval [0,…

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Q: Find the equation of the tangent line to the graph of the functic f(x) = 3x² - 4x +5 at the point…

A: Find out the equation of tangent line.

Q: Which of the following is a parameterizatino of the line that passes through the point (5, 4) With a…

A: Let's find.

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: Find all critical values for the function f(x) = (3x+7)/((x^2)+x+1) and the list them seperated by…

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Q: Given q(x) = x – 4x2 + 10, find the x-coordinates of all local minima using the second derivative…

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Q: Find all the value(s) of x at which f(x)=10x33+13x22+4x+16 has a horizontal tangent line. If there…

A: we will  find value of x at which at f'(x)=0

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Consider the given function y=131-x2 It can be write as y=131-x12

Q: A curve through the point Q(4,3) has the property that the sum of the distances from each point on…

A: The distance between the points and is given by the expression . If 2 lines are perpendicular,…

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: (b) : Verify that the Intermediate Value Theorem applies to the indicated interval and find the…

A: Given , f(x)= x²-x in the interval [1,5]

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: y=x-4x The domain of given function is [0, ∞). Differentiating with respect to x, we get…

Q: Given q(x)=x4 −4x2 +10, find the x-coordinates of all local minima using the second derivative test.…

A: The given function is q(x)=x4−4x2+10.

Q: Consider the function f(x) = 2x² + 5x – 1 on the closed interval [- 3, 2]. Find the exact value of…

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Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: Find the critical points of f(x) = -2x + 2x2 - 8 and apply the Second Derivative Test (if po < of…

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Q: Find all critical points of the function  f(x)=x^(3)+4x^(2)−5x+6. If there is more than one…

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Q: At what point on the curve xy=x*+5x is its tangent lines .. a.) parallel to the line 12x-y=…

A: The equation of the given curve is xy=x4+5x By dividing both sides by x, we get y=x3+5 To find the…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A:

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 4. Find the intervals in which the function f(x) =x³ – 6x2 +9x +30 is concave up/concave down. Also…

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Q: Which of the following is a critical point on the curve y = x3 − 3x2 + 4x + 5

A: SOLUTION-

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: - The equation f(x) = Inx-x +3 has a root in the interval (4,5). Obtain the roo correct to three…

A: Given function is, fx=ln x-x+3 in the interval (4,5) First iteration: Here f4=0.3863&gt;0 and…

Q: Given q(x) = x – 4x2 + 10, find the x-coordinates of all local minima using the second derivative…

A: Given that,  qx=x4-4x2+10q'x=dqxdx         =ddxx4-4x2+10         =4x3-8xq'x=4x3-8x=4xx2-2=4xx-2x+2

Q: Determine the linear fünction whose graph satisfies the given criteria. Passes through the point…

A: Given: a point (-9,2) and a line 3x+2y=12Formula:For a given line…

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

A: Given f(x,y)=x3-y2-48x+8y

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: 3. Use the Intermediate Value Theorem to prove that the equation x-5x = 4 is solvable on the…

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Q: Find the value of c guaranteed by the Intermediate Value Theorem. F(x) = x^2 -4x + 7, [4,8], f(c) =…

A: We have to find the value of c

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: Which of the following is a parameterization of the line that passes through the point (-1,–6) with…

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Intermediate Value Theorem: It states that if f is a continuous function whose domain contains the…

Q: The function f(x) = (6x + 9)e-6z has one critical number. Find it.

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: To find the critical numbers, first find the derivative of f(x) then set the derivative equal to…

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. kx2…

A: The given family of curves is kx2+y2=1. Differentiate both sides of the above equation with respect…

Q: Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) = (x…

A: The fixed-point iteration method uses the formula: xn+1=ϕ(xn) to perform the iteration and to…