1 Find the intervals in which the function f(x)==x*- is concave up/concave +-x 3 down. Also find the inflection points, if they exist.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: The function f(x) = x* - 18z is increasing on the intervals

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Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…

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Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Given function is fx=x2-6x+5. Critical numbers of a function is the point where its first derivative…

Q: 4. Given f"(x) 2x(x²-3) 2+1) find all intervals of concavity and x-values of any inflection points.

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Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

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Q: Find the intervals where f(x) = x2e−x is increasing and where it is decreasing.

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

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Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: f(x)=(x-1)2(x+3) To find out critical numbers , we take derivative and set it =0 apply product rule…

Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x>5 We have to find the value…

Q: Determine the intervals of concavity and inflection points, if they exist, for 1 f(x)=; 1+x Use…

A: Given: f(x)=11+x2 We have to determine the intervals of concavity and inflection points, if they…

Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

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Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

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Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Derivative of a function determines the change of a variable with respect to another variable. First…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: f(x)=ln 5x2+4x2+1

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given: f(x)=x29-x2 To Find: Intervals of increasing and decreasing on (-3,3). Concept: (a). if…

Q: Find the x-value(s) where the function f(x)- xS2 is not differentiable x-1 x>2 Give a reason for…

A: Consider the given function fx=xx2-1,    x≤2x-1,        x>2. Sketch the graph of the given…

Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

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Q: 2. Use the second derivative to determine the intervals where f(x) = -2x³ + 4x2-150x is concave up…

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Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Given: fx=-3x2-4x-2

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: The critical points of the function are the points where the function is defined but its first…

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

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Q: Find the open intervals where the function f(x)=-2/x+1 is concave up and concave down. State any…

A: According to the given information, it is required to calculate the interval where the function is…

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

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Q: 2) State the intervals of concavity in the function f (x) = x3 + 2x2 – 4x + 5.

A: We have to determine the intervals for concavity of the function: fx=x3+2x2-4x+5 To check the…

Q: Determine the intervals of concavity for the function f(x)=e^(-x)- e^(-(-3x).You must use exact…

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Q: For the function f(x)=6x+2sin(x)f(x)=6x+2sin⁡(x), find all intervals where the function is…

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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: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

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Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

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Q: Suppose f'(x) < 2 for all x 2 2, and f (2) = 7. Show that f(4) < 11.

A: Given that f'x &lt;2 for all x≥2 and f2=7.We need to show that f4&lt;11.

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: 4. Find the intervals of concavity for the function f(x) = e-/3. Identify any inflection points.

A: use double differentiation =0 to find inflection points and concavity

Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

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Q: Find the intervals of monotonicity of the function f(x)=x2e−x.

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Q: 11. Determine the absolute extreme values of f(x) = xe-/2 = xel-/2 on the interval [0, 5].

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Q: 6x + 7, on the Find all absolute and relative extreme values of the function f(x) interval [1, 4].…

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Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

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Q: 9. Given the function f(x) 3x*-4x2 +2, use the first and second derivative tests to find: a) the…

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