This is the graph of
𝑓
′
(
𝑥
)
.

Which of the options (A, B, C, D) shows the graph of
𝑓
(
𝑥
)
given that
𝑓
(
0
)
=
2
?

Question

This is the graph of 
𝑓
′
(
𝑥
)
.

Which of the options (A, B, C, D) shows the graph of 
𝑓
(
𝑥
)
 given that 
𝑓
(
0
)
=
2
?

BlackTom AI · Accepted Answer

Let's restate what we know and what we would need to determine f(x).
- We are given the graph of f'(x). To obtain the graph of f(x), we would integrate f'(x) and then use the initial condition f(0) = 2 to determine the constant of integration.
- In practice, for each candidate option (A, B, C, D), we would check whether the proposed f(x) has a derivative f'(x) that matches the given graph. This involves verifying:
  1) The slopes and sign of f'(x) on each interval corresponding to the segments of the f'(x) graph.
  2) The continuity and any corner points where f''(x) (the derivative of f') would change sign or magnitude.
  3) That f(0) equals 2 after integrating f'(x) and applying the constant of integration so that the value at x = 0 is 2.
- However, the answer options (A, B, C, D) are not provided in the prompt you shared. Without those specific candidate functions, we cannot compare them directly or confirm which one matches the integrated form of f'(x) with f(0) = 2.
- If we had the explicit f'(x) graph in terms of piecewise definitions (for example, f'(x) = m1 on interval I1, f'(x) = m2 on I2, etc.), we would:
  • integrate on each interval to obtain f(x) up to a constant,
  • apply f(0) = 2 to determine that constant,
  • then compare the resulting f(x) against each candidate option to see which one has the same expression and matches the value at x = 0.
- In short, to proceed, we need the four answer options (A, B, C, D) or at least a description of each proposed f(x). Once those are provided, I can give a detailed, step-by-step comparison explaining why the correct option matches the integrated form of f'(x) and satisfies f(0) = 2, and why the other options do not.

MATH-112-301-001 Unproctored Midcourse Exam 4 Practice Exam 1

This is the graph of 𝑓 ′ ( 𝑥 ) . Which of the options (A, B, C, D) shows the graph of 𝑓 ( 𝑥 ) given that 𝑓 ( 0 ) = 2 ?

查看解析

登录即可查看完整答案

类似问题

If 𝑦 = ln ⁡ ( 5 𝑥 − 1 ) 4 then 𝑑 𝑦 𝑑 𝑥 =

Find the velocity at t = 0.69 using the following equation defining position. p(t) = 2t3 - 4t2 +11t -2 Round to 2 decimal places.

Differentiate [ ln ⁡ ( 3 𝑥 ) + 5 ] 2

Differentiate cos 3 ⁡ 4 𝑥

Differentiate 𝑒 3 𝑥 2 + 5 𝑥

Differentiate ln ⁡ ( 𝑥 2 − 5 2 𝑥 + 1 )

Differentiate ln ⁡ ( 7 𝑥 + 5 )

Differentiate cos ⁡ ( 3 𝑥 )

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单