38. Given that 0 < a < b, let f (t) = 1 if a

Q: Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that…

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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. 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: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that…

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Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

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Q: Find all critical points of the function. f(t) = t - √(t + 1)

A: The critical point of the function f(t)=t-t+1 is obtained by equating the first derivative of the…

Q: Q5: a- Use two segment trapezoidal rule to integrate the following function numerically: f(x) =…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

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: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

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Q: 2. If f is differentiable at a, then Duf(a) = Vf(a) · u. Moreover, if Vf(a) + 0, it gives the…

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Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 1. If f(x)=∫0 to x(t^3+6t^2+5)dt then f″(x)=

A: Topic = Derivative As per guidelines , at a time only one question can be answered out of different…

Q: Given a function f(x) that is continuous and differentiable, and a point a in its domain, we…

A: This question can be solve by taking approximation as x tends to a (more close)

Q: The function f has a continuous second derivative, and it satisfes f(2) = 5, f'(2) = 0 and f"(2) =…

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Q: Suppose f(x)=-3x2+2x+2 and a position of particle is moving by s(t) at time t such that: a)Find…

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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: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

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Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

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Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

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Q: 4 ース -where do es t have relahive minimums ? the relahi ve minimum is which occuRs at X= where does…

A: topic- relative maximum and minimum of function  relative minimum is the value of function where…

Q: We want to study the following function on the interval I = [-2; +[ %3D 3x? + 4x +3 g(x) : %3D x² +…

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Q: 4. A company possesses a major piece of equipment that denigrates at a continuous rate f =f(t),…

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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: Compute G' (x), G" (x), and deduce the intervals of increase or decrease of G, its local extrema (if…

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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: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: Q1: From the given graph of f(x) = sin x; [0 ,27] , f ind: (a)The critical points. 211 -2…

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Q: If f(x) = In(tanh(2x)), then f' (x) is Select one: a. -2 coth(2x)sech (2x) :): b. – coth(2x)sech (2x…

A: f(x)=ln(tanh(2x))f'(x)= 1tanh(2x) ddxtanh(2x)we know that  tanhx=ex-e-xex+ e-x…

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: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: 2 The reliability of a turbine blade is given by R(t) = to, where to is the maximum life of the…

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Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

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Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

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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: The tangent line to y=f(x) at (7,0) passes through the point (6,−7). Compute the following. a.)…

A: Topic:- calculus

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: function, that is 0 everywhere except at t=0, is know as:

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Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &amp;  f"(x)=12x2

Q: #8

A: Given:The decrease in weight from 487 pounds to 130 pounds in 8 months.