Let f (x) = x3 − 7x.Find all numbers c in the interval (-3, 0) for which the line tangent to the graph of fis parallel to the line joining (−3, f (−3)) and (0, f (0)). How many such numbers exist in the given interval?     Enter the numbers in increasing order, with the smallest first. (The smallest is negative!) Enter DNE in any extra answer blanks.

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: let f(x)=ex for 0 < x < 1 Approximate f(0.25) using linear interpolation with x0=0  and x1=0.5 .…

A: Substitute x0=0 and x1=0.5 in fx=ex  and calculate L0(x) and L1(x), to construct the Lagrange…

Q: Find the critical numbers of the function. f(x) = x² log,(x? + 2)

A: fx=x2log7x2+2⇒fx=x2logx2+2ln7      ∵logab=logblna Critical numbers are the values of x for which…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

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. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

Q: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

A:

Q: Let L(x) = ln(x² + 4x + 14) in the interval [-10,10]. What are the absolute extrema of L(x) in this…

A:

Q: 3. Given f(x) = x³ + x² – x + 1, on the interval bsolute maximum and minimum values, and indicate…

A:

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

A:

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

A:

Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

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

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Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

A:

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

A:

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

A:

Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

A:

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

A:

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: Find the x-value corresponding to the absolute minimum value of f on the given interval. (If an…

A:

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

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: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

A: Given that f is continuous and f13f(x)dx=8 To prove line y=4 intersects the graph of f altleast can…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 When is the function concave up and concave down in…

A: For concavity we need second derivative.

Q: Let f(x) = 18xe - 1s. (a) f'(x) (b) Solve f'(x) = 0 to determine the critical values of f.

A: Recall: (uv)'=u'v+v'u

Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

A:

Q: The absolute maximum of y =-x + 2x +3 on the interval [0, 3] occurs at Select one: O a. None of…

A: Simply take the derivative and equate to zero than solve for x.

Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

A: Given,  fx = x2-4x+9    We have to find the absolute extremum values in the interval 1, 4

Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

A:

Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 10 over the interval [1, 3].

A:

Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

A:

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8