Practice

Applications of derivatives

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Find the relative extrema of each function

Find the concavity and inflection points

Compute using L'Hôpital's rule

Find the absolute extrema on the interval

Problems

Answers

Local maximum at (1,5); local minimum at (3,1).
Minimum at (3,-27); there is no extremum at x=0.
Maximum at left(1,frac1eright).
Minimum at left(frac1e,-frac1eright).
Minimum at (2,4).
Maximum sqrt2 at x=(pi)/(4); minimum -sqrt2 at x=(5pi)/(4).
Inflection at (1,0); concave down on (-infty,1), concave up on (1,infty).
Inflection at x=pm1; concave up if |x|>1, concave down if |x|<1.
Inflection at x=pm(1)/(sqrt2).
-frac16
0
0
Absolute maximum 3 at x=2; absolute minimum -1 at x=1.
Absolute maximum 4e^-2 at x=2; absolute minimum 0 at x=0.
A 10times10 m square, with maximum area 100 textm^2.
x=2 cm and V_max=128 textcm^3.
It moves down at frac98=1.125 m/s.
(dr)/(dt)=(1)/(pi)approx0.318 cm/s.
sqrt(26)approx5.1 (true value 5.0990).
c=(2)/(sqrt3)approx1.155.