x- 4 ,x<5 Given: f(x) = - , find the value of k that will make f continuous on (-0,x) kx2 – 24x + 46 ,x>5 А 5 B c) none of the given choices D) -4 E

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0&lt;x≤b6/x   ,        x&gt;b

Q: 2) Consider the function g(x) = x3 + 3x2 – 9x + 2 on the interval [-4,2]. Find all local extrema,…

A: According to our company policy we can only answer the first question and rest of the questions can…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax – b -1 < x< 1, x 21 Continuous at x-0

A: from given function , the value of function in between 1 and -1 is ax-b. As x approaches to 0 the…

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 8 2. Find the absolute extrema, if they exist, as well as where they occur for f(x) = 2x + + 1, x >…

A: Given function  f(x) = 2x + 8/x2 + 1      , x&gt;0  To find the absolute extrema, let's find the…

Q: 2/ Solve: (2 Sin () + C 2x-3 Then, Find the amount of (C) that is make the function continuous at x…

A: A function f(x) is continuous at x=a if (i) f(a) is defined (ii) limx→af(x) exists(iii)…

Q: 2) Consider the function g(x) = x³ + 3x2 - 9x + 2 on the interval [-4,2]. Find all local extrema,…

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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: 3. At which points of R? is each function continuous? Explain your reasoning. (a) f(x, y) = cos(xy+…

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Q: Suppose f is differentiable and (-1,4) is a point on the graph of f. The estimate f(-0.8) 5 is…

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Q: 7. If g(4) = 3k +7, g(9) = 7, g' is continuous and %3D J g'(x)dx = 2k? + 13, find the value of k.

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Q: Given that f(x) = -x +12x – 34 has a relative maximum at x = a. f' is negative on the interval (-…

A: Given query is to find the correct option for the f(x).

Q: 13. A differentiable function f on the interval -2 sxs7 is such that f'(c) = 0 where -2 <c<7. If…

A: Clearly we have, f'(c) = 0. Means c is a critical point.

Q: +5, x <-1 Given f(x) = 3-x, -1< x s 1 x2+2, 1<x<2 X- Wx-2 + 4, x2 2 Find the point(s) where f(x) is…

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Q: Consider a differentiable function f(x) :[-, →R such that f' (x) = 32? – 3 and f(0) = 1. Which one…

A: We need to choose correct option.

Q: my (x, y) # (0,0) x2+y2 f (x, y) = (х, у) - (0,0)

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Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

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Q: 2) Consider the function g(x) = x³ + 3x? – 9x + 2 on the interval [-4, 2]. Find all local extrema,…

A:

Q: The point (a,b) is the critical point of the function f(x,y) = xe" +6y-7x+21 Find the value of a.

A: Given : fx,y = xey+6y-7x+21

Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

A: Given that, f(x)=15x-5sin3x2x3, x≠0c,                          x =0 The function is continuous when…

Q: Q#3 Find the absolute maximum and minimum values off on the given closed interval, and state where…

A: Given: fx=x-2 sin x; -π4&lt;x&lt;π2 For finding the absolute maximum and minimum first find the…

Q: Verify that the given family of functions is a solution of the DEQ. Assume an appropriate interval I…

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Q: 1) Find the interval(s) where f(x)= 12 x3 -x+6 is concave up and concave down . Also find the…

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Q: 4x in the interval 0,10]. [0,1]. Find the absolute extrema of f(x) = x² + 1 4x [o,10]

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Q: According to the function Vx + 2 shown, which statement provides a true conclusion? -1.6 08 0 0.8…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: and apply the First Derivative Test to each critical point. Let -64 f(x) = x* + 20x3 + x² – 320x %D…

A: Given,f(x)=44x4+203x3+-642x2-320xf(x)=x4+203x3-32x2-320xdifferentiating both the sides with respect…

Q: 1. Determine the intervals of the domain where each function is continuous. Use appropriate interval…

A: (1). (a).  The given function is: h(t)=t2-9-1

Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

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Q: The second derivative f" is defined on the closed interval [0, 8n]. Now test f" in the intervals (0,…

A: use the definition of concave upward and concave  downward .

Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

Q: 2x2 – 20x – 7 on the interval (3, 7), how many values of If we apply Rolle's Theorem to the function…

A: We have to apply rolles theorem

Q: (0) On the interval [6, 9], / f(x) dr %3D

A: Integration of f(x) on the interval [6,9] is given by:

Q: 16 8. If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A: Given integral, ∫016f(x) dx =18

Q: Find a and b such that f is differentiable everywhere.

A: The given piecewise function is: fx=ax3,      x≤2x2+b,   x&gt;2 This function is differentiable…

Q: The point (0, 0) is the critical point of the function f(x, y) = Select one: O True O False x²y 2 +…

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Q: he graph of f(x) - x+1 is concave down on interval OA (-1,1) Ов. (0,1) Os. (-m 0LI(? m)

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Q: a.) On the interval (-o, 0), f"() b.) On the interval (0, 0), f"(x) = Thus, c.) On the interval (-o,…

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Q: 7. If f(4) f '(x) dx = 15, what is the value of f(7)? 14 11, f'is continuous, and %3D f(7) =

A: Given

Q: 9. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x³ – 2x2 – 5x + 6 on…

A: We have to find the value of c the solution is following

Q: 4 For what value(s) of x is the function f(x) х? — х — 12 NOT continuous? A. x = 3 and x = -4 В.…

A: Given function is  f(x)=4x2-x-12

Q: Determine where f'(x) exists, an expression for it, and where f'(x) is con- tinuous: f(z) = { 0…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: Find the linearization at x = a. f(x) = sin3 (x), a = 4 (Use symbolic notation and fractions where…

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Q: Find the absolute maximum and minimum values of f(x) =z-3x2 +2 nterval -1, 1]. Hint: be sure to…

A: Given query is to find the absolute maximum and minimum for f(x).

Q: Find the absolute extreme values of the function on the interval. 14) f(x) = ex - x, -1 sxs 2 %3D

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Q: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: (4x³ + 42x)(x² + 7)² - (xª + 21x²) · 2(x² + 7)2x (x² + 7)4 (G) f"(x) %3D 14x(21 – x²) (x² + 7) Since…

A: if f"(x) = 0 then point of inflection roots of x

Q: Find a value of the constant k, if possible, that will make the function continuous everywhere.…

A: