6. True or False The graph of the function f(x) = x? is increasing on the interval (0, ). (

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

A:

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…

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A:

Q: If f(x)=tanh(3x)f(x)=tanh(3x) then f'(x)=f′(x)=

A:

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

A:

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

A:

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

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: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: 2) Suppose the graph of f (x) and the graph of its derivative f '(x) are shown below. Find an…

A: From the graph of f(x) , at x=1, f(x)=1 From the graph of f'(x), at x=1, f'(x)=-2

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

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: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Suppose that f is a differentiable function with f(2) = 5. If the tangent line to the graph of y =…

A:

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: 5. What is the definition of the derivative of a function f(x) ?

A:

Q: are correct? The function is decreasing on the interval x > 4.

A: According to graph for x&gt;2 slope = dydx increasesSo the function is increasing on the interval…

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: 2) Suppose the graph of f (x) and the graph of its derivative f'(x) are shown below. Find an…

A:

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: Find the intervals of increasing and decreasing, and intervals of concavity for f(x)=x^2/3(x-4) Do…

A:

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: I'm confused on how to put a piecewise function into interval notation

A: To rewrite the definition of the given function using interval notation

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: 2. Use the second derivative to find the inflection points and the intervals on which f(x) is…

A: For inflection point, Put f"(x)=0. For concave upward, f"(x) &gt; 0. For concave downward, f"(x)…

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: What is the derivative of the exponential function a x, a &gt;0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

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: 26) The interval where f(x) is decreasing is?

A: Answer and explanation is given below...

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

A:

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…

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…