3.2. Extrema and the Mean Value Theorem http://www.ck12.org
In problems #4–6, find the extrema and sketch the graph.
- f(x) =−x^2 − 6 x+ 4 ,[− 4 , 1 ]
- f(x) =x^3 −x^4 ,[ 0 , 2 ]
- f(x) =−x^2 +x^42 ,[− 2 , 0 ]
- Verify Rolle’s Theorem by finding values ofxfor whichf(x) =0 andf′(x) = 0 .f(x) = 3 x^3 − 12 x
- Verify Rolle’s Theorem forf(x) =x^2 −x−^21.
- Verify that the Mean Value Theorem works forf(x) =(x+x^2 ),[ 1 , 2 ].
- Prove that the equationx^3 +a 1 x^2 +a 2 x=0 has a positive root atx=r,and that the equation 3x^2 + 2 a 1 x+a 2 = 0
has a positive root less thanr.