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Q: We note that F is continuous for all x, and its derivative is (x-1) if x>0 F'(x)= -1 if xr<0 The…

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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: Find the limit, if it exists. V(t + 25)(t – 1)² lim 11t - 11 t-1+

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Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x&lt;014x-1       x≥0 To check whether…

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

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: QUESTION 2 Let f(x) be a function with second derivative of f"(x) =(x+8)(7x –11)(x – 13). Determine…

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Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

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Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

A: Answer

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. Below is the graph of f(x) = |x]. Using the left side of the function with the equation y = – x,…

A: The graph of f(x)=x is given

Q: (a) Suppose that the first derivative of the function y = f (x) is given by f'(x) = 6(x +1)(x – 2)²…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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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: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: 55. By normalizing the function f(x)==-defined in the domain [0, 2], we will get as a result the…

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Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

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: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

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Q: 19 – x² ; if x 3 continuous or not on the interval [0, 3].

A: Given function: fx=9-x2;if x≤3x-3;if x&gt;3 The objective is to determine if the function is…

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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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: 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: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: Klein is located on the tangent line to y=3x2 -x  at x = 1.

A: Using , slope point formula

Q: (2+) ( 29 3 7. Suppose that lim In .Fill in the boxes for the corresponding equation involving the…

A: 7.  limn→∞∑i=1n2+3in2+3in2+4.3n=12ln268

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

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Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

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Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) f'(x) > 6 for all x. = -2…

A: Given, fx is differentiable everywhere. f-4=-2 f'x≥6, for all x dydx≥6, for all x  dy≥6dx…

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: 1. Find all the local and global extrema of the function f (x) = sin(x) – x [-27, 27]. Clearly…

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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: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: Гa+ 4x ifx 1 Let f(x) (a) The value of a that will make f(x) continuous for all real numbers is a =…

A: Check the differentiability of a function when it is continuous at x= 1 .

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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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: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…