8) E.C. sketch the graph of the function thot satisfies all of the qiuem an glom andition S foif Ix|<4 flw4 x) > it4)=0 lim

Q: Given function f with f'(x)= 4-4x^2 / (x^2+1)^2 and f''(x)= 8x^3-24x / (x^2+1)^3 (a) Given the…

A: Given, f'(x) = 4-4x2(x2 +1)2  f''(x) = 8x3 -24x(x2+1)3 (a) If f is concave up then f''(x) &gt;0 So,…

Q: f(x)=-(x-1)2 use f'(x) to find decreasing interval

A: f(x)=-(x-1)2 = - (x2 - 2x + 1) = 2x - x2 - 1

Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

A:

Q: If f(q)  = 50 + 50q gives profit when selling q units, and g(t) = t^2 - 12t + 1 gives the quantity…

A: Given: f ( q ) = 50 + 50 q , where f ( q )  is the profit on selling q units. g ( t ) = t 2 – 12 t +…

Q: Show the graph that satisfies all of the given conditions. Please explain your answer.  f'(-2) =…

A:

Q: Find the derivative of f(x) = 33x-1 O 33x-2 In3 O 33x-1 In3 33x In3 32x In3

A: (1). Given: fx=33x-1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: sketch a graph with these restrictions. Label any max/min points and any point of inflections

A: Step 1: Step 2: Step 3: Step 4:

Q: Find f'(x). f(x) f'(x) = 120x¹4 - 27x² 8x15 - 9x³ + 8 = Compare the graphs of f and f' and use them…

A: The given function is

Q: determine the f(0) if f'(x) = 2cosx + 8x^3 + e^x

A:

Q: Find the increasing and decreasing intervals of the function f'(x)= -3/(x-1)2. Then find the local…

A: f'x=-3x-12

Q: In each part, list the points (A–F) on the graph of f whose x-coordinates satisfy the given…

A: Given data: The given graph is shown. Point A on the graph has zero slope and maximum value of the…

Q: Sketch the graph of a function that satisfies all the given conditions.

A: We have to sketch a graph satisfying the given condition.

Q: Sketch a graph with the following characteristics: f'(x)>0,  -inf3 f"(x)>0,  0<x<2,  4<x<inf…

A: Given  (i)f'(x)&gt;0   for   -∞&lt;x&lt;-1,   1&lt;x&lt;3 The graph is increasing in the intervals…

Q: Sketch the graph of a function that satisfies all of the given conditions. f'(0) f'(x) > 0 if x 4,…

A:

Q: Suppose that Find f'(2). f'(2) = f(x) = = e³x x² + 4

A: Given f(x)=e3xx2+4   We are required to findf'(2)         The following formulas of derivatives has…

Q: if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0 f(3+5x) + f(3+6x)/x

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.