31. f(x) = –x² + 5 -2 -1 012 f(x) 32. h(t) = }|1 + 3| - 5 -4 - 3 -1 h(t) |-x + 4, x s 0 (x – 2)?, x > 0 33. f(x) = -2 -1 0 1 2 f(x) [9 – x², x < 3 - 3, x 2 3 34. f(x) 1 2 3 4 5 f(x) 2.

Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: x-1 2. Find the critical numbers of f(x) =- %3D x +4

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Q: Find the critical number for y = f(x) = x (x + 2)²

A: NOTE: Refresh your page if you can't see any equations. . the given function is take derivative…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local…

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Q: Find the values of a and b such that f(x) = x³ + ax² + bx + 5 has x = 1 and x = 2 as critical…

A: The function f(x)=x3+ax2+bx+5 has critical points at x=1 and x=2

Q: 3) The function f(x) = e*(x² + x - 1) has derivatives f'(x) = e* (x2 + 3x), f"(x) = e*(x² + 5x + 3),…

A:

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

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Q: 38 Find the critical numbers of the function. 25. f(x) = x³ + 3x² – 24x %3D -

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Q: 7 Determine a value for r so that h(x) x + rx² – 7x has an inflection point at x = 5. 2 -- |

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Q: 22. (a) Find the critical numbers of f(x) = x*(x – 1)°. (b) What does the Second Derivative Test…

A:

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x +5 on the interval [0, 3].

A:

Q: 2 3 Use the first derivative test to determine the local extrema, if any, for the function f(x) =…

A: Take the derivative of f (x)  and equate to zero for finding point of extrema.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: 2. Find the absolute minimum and maximum of the function f (x) = – 2.22 on the interval [-2, 1).

A: We have to solve

Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: (3) Find the absolute maximum and minimum values of f(x) = x³ – 3x – 1 on the interval [0,3).

A:

Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

A:

Q: Find all FIRST and SECOND order critical POINTS for f(x) = (x² +x – 2)'/3

A: fx = x2+x-213f'x = 13x2+x-213-1 . ddxx2+x-2        = ddxx2+ddxx+ddx-23x2+x-223        =…

Q: 1. Consider the function F(x) = x³(x – 2)². a) Find all x values where F'(x) = 0 or F'(x) does not…

A: Critical numbers.

Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: f(x,y)=x2+4xy we have to find the critical points.

Q: 1. (a) Find the critical point(s) of the function f(x) on the interval -4,4. x2 +4 1. (b) Use your…

A: Critical point and the absolute minimum is determined as shown below

Q: 1. f(x) = 3x + 4, at x = 4 2. f(x) = 3x2 – x + 2 at x = 2 3. f(x) = ***, at x = 1 x+3 4. f(x) = X-1…

A: As per guidelines we can solve only three subparts at a time, so the first  three subparts can be…

Q: Find the local extrama of f(x)=x²-8x+12 on a closed interval [-2,5] O a. minimum value at x =4 is -4…

A: Topic- application of derivatives

Q: 1-e2x 10. lim X0 1-ex x2-3x-28 4. lím エ→アーx-14x+49 11. lim In(x sin x) ズ→0 5. lim V2x + 1T ズ→4 12.…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: 12 11. Find the critical points of f(x) 4x? ). Then use the Second Derivative Test to determine if…

A: Here, we need to find the critical points of f(x)=x127x3-4x2. Now, f'(x)=6x2x-10xx and…

Q: EXAMPLE 6 Discuss the curve y = 3x* - 48x³ with respect to concavity, points of inflection, and…

A: If fx=3x4-48x3, thenf'x=12x3-144x2=12x2x-12f''x=36x2-288x=36xx-8 To find the critical numbers we set…

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: Determine all critical points for the function. 3 12x 2 Ox= -2 Ox=-2, x = 0. and x = 2 Ox= 2 Ox= -2…

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Q: If f (x) =x2-6x+2, find the maximum and minimum values of f on the closed interval [-3,4] Oa f (x)…

A: To find: The maximum and minimum value of the function is fx=x2-6x+2. Concept used: Power rule of…

Q: 8. Use the fact that the critical points of f(x, y) are found when vf(x,y) = 0 to show that (-3,-2)…

A:

Q: Q 3) Find the critical numbers of f(x) = x4(x - 1). Derivative Test' tell you about the behavior of…

A: given information function

Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

A:

Q: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 3 The absolute minimum of f(x)= 3 x³ - 2x 0n [-1,8] is y =

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Q: 1 - X 0 3

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Q: x = -1 is a critical number for g(x) = xª +x³ +x - 1. But the second derivative test fails for x =…

A: Explanation of the answer is as follows

Q: (i) Show that the line y = 2x – 2 always intersects the curve y = nx² + 6x -n at two distinct points…

A: To solve the problems

Q: 3/ Find the critical numbers of the function f(x)= x/5 (4-x)

A: The given function f(x)=x354-x

Q: 11. Find the absolute minimum and maximum of f(x) = x³ – 4x2 – 3x + 3 on the interval [0, 4].…

A: Given: fx=x3-4x2-3x+3; x∈0,4 for finding absolute minimum and maximum of given function, we draw…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: The function f(x)=2x^3−27x^2+48x−6 has two critical numbers. The smaller one is x =   and the…

A: The given function is f(x)=2x3-27x2+48x-6                           Differentiate with respect to x,…

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

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Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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Q: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: Find the critical numbers of the function f(x) = 2x -15x2 +36x- 24. O a. -2 and -3 O b. 2 and-3 O c.…

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Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

A: