The following graph shows f'(x). On what interval is f(x) decreasing? 12 20 28

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: The above is the graph of the derivative f '(x). How many critical points does the original function…

A: From the graph of function f'(x), number of roots of f'(x) are three. Let f'(x)=ax3+bx2+cx+d

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: In the given equation/s as follows (a) find the critical numbers of f, if any, (b) find the open…

A: (a) Consider the function f(x)=-7x3+21x+3 to find the critical numbers of f, set the first…

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Q: Find the approximate value of derivative f′(0) with the step size h for the following function by…

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Q: Consider the function f(x) =3 on the interval [1,5]. A graph of the function appears to the left.…

A: SOLUTION-

Q: 2. At x 3, the tangent line to the graph of a function f (x) is y = 4x + 5. What is f'(3)? How do…

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Q: 3. Below is the graph of y = f'(x), which is the derivative for some function f. Using the graph of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: - Is the function given by G(x) = Why or why not? continuous at x = 0?

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: In the given equation/s as follows (a) find the critical numbers of f, if any, (b) find the open…

A: Given, f(x)=x23-4

Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes…

A: Given,

Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: The second derivative for the following function at x = 2 f(x) = v2x + is O 1 O 1/4 O 1/2 O 3/4

A: Use the basis concept of integration and derivative than simplify.

Q: Let f(x)=x² – 3x'. For what value(s) of x in [–1, 1] is the slope of the line tangent to the graph…

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Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: Answer the following questions about the function whose derivative is f'(x)=(x-5)^2(x+7). a. What…

A: (a) For critical points:

Q: Find the function with the given derivative whose graph passes through thế polnt P. f (x) = 2x – 3,…

A: Given function: f'x=2x-3 And passes through the point P3,4

Q: 4 Given the function f (x) = :3 using the limit shown below. You do not have to simplify your…

A:

Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

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Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: The Range Rf for the functionf (x) = tanhx is:

A: Range of f(x)= tanh x

Q: The second derivative for the following function at x = 2 f(x) = V2x + is O 1 O 1/4 O 1/2 3/4

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Q: On what interval is the function f(x)=x^2e^x concave downward?

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Q: 3. Below is the graph of a function f(x) on the interval [0, 6]. Sketch the graph of its derivative…

A: Given the graph of f(x) on the interval [0, 6] To obtain is graph of f'(x)  on the same interval [0,…

Q: In the given equation/s as follows (a) find the critical numbers of f, if any, (b) find the open…

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Q: The graph of a function f is given. YA Estimate 10 [20 1 0 1 f(x) dx using five subintervals with…

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Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

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Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

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Q: The graph of the first derivative of a function is shown a) How can we know in which intervals the…

A: Here we have the graph of the first derivative of a function is shown.

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

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Q: Suppose the only information we have about a function fis that f(1)=2 and the graph of its…

A: Ti find the linear approximation.

Q: -) Givea the following data table= 国间。间 28 f(x.)- X, 2 42 3 50 Use Second-order finite difference to…

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Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: he tangent line to y= f(x) at (-7, -6) passes through the point (-9, -2). Compute the following.  a)…

A: GIVEN DATA : Equation y=fx                         Tangent of the y=fx at -7,-6 passes through the…

Q: Differentiate the function below y = ln ( ( etan x √(x2 +1) )  /  (x-3)5)

A: We first simplify the given function.  y=lnetanxx2+1(x-3)5y=ln(etanx)+lnx2+1-ln(x-3)5  [addition and…

Q: The graph of the second derivative of a function f(x) is shown at right. Which of the following…

A: Given graph is

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

A:

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.

A:

Q: Let f(x) = 21 – x² The slope of the tangent line to the graph of f(x) || at the point (-4, 5) is The…

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Q: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15…

A: Given: f(x)=x+1 at a=15

Q: On the graph of f(x) = sec x and the interval [0, 2Δ), for what value of x does f(x)= -1?

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Q: Find the higher order derivatives for f (x)=x^5, what is f^(6) (x)?

A: According to the given information f(x) = x5 and it is needed to calculate f6(x).Since, if p(x) is a…

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s

Q: 10.The graph of f'(x), the derivative of f, is given below for -6 Sxs7.On what intervals is the…

A: Option (c) is correct Because f'(x) is greater or equal to zero in that interval. Or we can say…

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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