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Section 4.3 : Minimum and Maximum Values
- Below is the graph of some function, \(f\left( x \right)\). Identify all of the relative extrema and absolute extrema of the function.
Solution
- Below is the graph of some function, \(f\left( x \right)\). Identify all of the relative extrema and absolute extrema of the function.
Solution
- Sketch the graph of \(g\left( x \right) = {x^2} - 4x\) and identify all the relative extrema and absolute extrema of the function on each of the following intervals.
- \(\left( { - \infty ,\infty } \right)\)
- \(\left[ { - 1,4} \right]\)
- \(\left[ {1,3} \right]\)
- \(\left[ {3,5} \right]\)
- \(\left( { - 1,5} \right]\)
- Sketch the graph of \(h\left( x \right) = - {\left( {x + 4} \right)^3}\)and identify all the relative extrema and absolute extrema of the function on each of the following intervals.
- \(\left( { - \infty ,\infty } \right)\)
- \(\left[ { - 5.5, - 2} \right]\)
- \(\left[ { - 4, - 3} \right)\)
- \(\left[ { - 4, - 3} \right]\)
- Sketch the graph of some function on the interval \(\left[ {1,6} \right]\) that has an absolute maximum at \(x = 6\) and an absolute minimum at \(x = 3\). Solution
- Sketch the graph of some function on the interval \(\left[ { - 4,3} \right]\) that has an absolute maximum at \(x = - 3\) and an absolute minimum at \(x = 2\). Solution
- Sketch the graph of some function that meets the following conditions :
- The function is continuous.
- Has two relative minimums.
- One of relative minimums is also an absolute minimum and the other relative minimum is not an absolute minimum.
- Has one relative maximum.
- Has no absolute maximum.