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 ?

View Explanation

Log in for full answers

Similar Questions

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 )

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler