2 out of 3
This problem challenges you to find cubic equations which satisfy different conditions.
1 out of 3
Sketch the members of the family of graphs given by $y = a^3/(x^2+a^2)$ for $a=1, 2$ and $3$.
1 out of 3
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
1 out of 3
What is the quickest route across a ploughed field when your speed around the edge is greater?
2 out of 3
Find the maximum value of n to the power 1/n and prove that it is a maximum.
3 out of 3
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
1 out of 3
1 out of 3
This problem challenges you to sketch curves with different properties.
1 out of 3
1 out of 3
Consider these analogies for helping to understand key concepts in calculus.
