Given that the graph of the derivative $f^{\prime }$ of a function $f$ is shown, which of the following statements is true about the function $f$?

Match the graphs of the functions in a–d with the graphs of their derivatives in A–D. <MATCH A-D IMAGE>

Analyzing Graphs

Each of the figures in Exercises 91 and 92 shows two graphs, the graph of a function 𝔂 = ƒ(x) together with the graph of its derivative ƒ'(x). Which graph is which? How do you know?

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Recovering a function from its derivative

b. Repeat part (a), assuming that the graph starts at (−2, 0) instead of (−2, 3).

Slopes on the graph of the tangent function Graph y = tan x and its derivative together on (−π/2, π/2). Does the graph of the tangent function appear to have a smallest slope? A largest slope? Is the slope ever negative? Give reasons for your answers.

Suppose the graph of the derivative $f^{\prime }$ of a function $f$ is shown. At which of the following points does the function $f$ have a local maximum?

Suppose the graph of the derivative $f^{\prime }$ of a continuous function $f$ is shown and $f^{\prime }$ is continuous everywhere. Which of the following statements is necessarily true about the function $f$?

Given the graph of the function $f\left(x\right)$ below, which of the following graphs best represents its derivative $f^{\prime }\left(x\right)$?

Based on the graph of $f\left(x\right)$, describe the graph of the derivative $f^{\prime}\left(x\right)$ on the interval $\left(0,\infty\right)$.