http://www.ck12.org Chapter 3. Applications of Derivatives
Review Questions
- Find all extrema using the Second Derivative Test.f(x) =x 42 +^4 x
- Considerf(x) =x^2 +ax+b,withf( 1 ) = 3.
a. Determineaandbso thatx=1 is a critical value of the functionf.
b. Is the point( 1 , 3 )a maximum, a minimum or neither?
In problems #3–6, find all extrema and inflection points. Sketch the graph.
- f(x) =x^3 +x^2
- f(x) =x^2 +x^3
- f(x) =x^3 − 12 x
- f(x) =−^14 x^4 + 2 x^2
- Use your graphing calculator to examine the graph off(x) =x(x− 1 )^3 (Hint: you will need to change they
range in the viewing window)
a. Discuss the concavity of the graph in the interval( 0 ,^12 ).
b. Use your calculator to find the minimum value of the function in the interval. - True or False:f(x) =x^4 + 4 x^3 has a relative minimum atx=−2 and a relative maximum atx=0?
- If possible, provide an example of a non-polynomial function that has exactly one relative minimum.
- If possible, provide an example of a non-polynomial function that is concave downward everywhere in its
domain.