Shown below is the graph of y = f ? ( x ) , NOT the graph of y = f ( x ) . (Clic

Question

Shown below is the graph of y=f?(x), NOT the graph of y=f(x). (Click on picture for a better view.)

Then from this information, we can conclude that the best approximation to f(?5.05)?f(?5) is

Shown below is the graph of y=g(x). Indicate the labeled point at which: (Click on picture for a better view.)
g(x) changes sign:
g?(x) changes sign:
g??(x) changes sign:

Shown below is the graph of y=f?(x), NOT the graph of y=f(x). (Click on picture for a better view.) Then from this information, we can conclude that the best approximation to f(?5.05)?f(?5) is Shown below is the graph of y=g(x). Indicate the labeled point at which: (Click on picture for a better view.) g(x) changes sign: g?(x) changes sign: g??(x) changes sign:

Explanation / Answer

1. Note that f ' (5) = 2

Thus f (5.05) is approximately f(5) + f ' (5) * 0.05

so f(5.05) - f(5) is about f ' (5) * .05 = 2 * .05 = 0.10

2. g(x) changes sign at d, since the function values go from negative to positive.

g'(x) changes sign at c, since g changes from decreasing to increasing there.

g''(x) changes sign at b, since the graph of g changes from concave up to concave down there.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.