Differentiation and Integration

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Sort these mathematical propositions into a series of 8 correct statements.

Can you find the maximum value of the curve defined by this expression?

Can you make sense of this combination of trig functions?

Can you hit the target functions using a set of input functions and a little calculus and algebra?

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

Can you rotate a curve to make a volume of 1?

Can you find the volumes of the mathematical vessels?

Find the relationship between the locations of points of inflection, maxima and minima of functions.

Consider these analogies for helping to understand key concepts in calculus.

Can you make sense of this relationship between function and derivative?

Which of these infinitely deep vessels will eventually full up?

This problem challenges you to sketch curves with different properties.

Can you match the charts of these functions to the charts of their integrals?