### Home > CALC > Chapter 3 > Lesson 3.2.1 > Problem3-45

3-45.

Below is the graph of a function $f(x)$ with tangents drawn at $x = -2$, $−1$, $1$, and $2$. $f^{\prime}(0) = 0$. Use the slopes provided in the graph to find the slope function $f^{\prime}(x)$. Also, find $f(x)$.

First make a prediction about the shape of the slope graph. The original graph is a parabola. What will the slope graph look like?

Next, make a table showing $x$-values and their corresponding slopes. Be sure to include that when $x = 0$, the slope is $0$ (after all, look at the horizontal tangent line).

Use your table to find an equation of the slope function.
{"extraction_info": {"found_math": true, "script_math_tex": 11, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7671242952346802, "perplexity": 394.60162861806384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00458.warc.gz"}