3.05 Using the first and second derivatives

Interactive practice questions

The gradient function of $g\left(x\right)$g(x) is $g'\left(x\right)=3$g′(x)=3.

Select all possible graphs of $g\left(x\right)$g(x).

Loading Graph...

Easy

1min

Sketch the linear function that satisfies the following information

$f\left(0\right)=1$f(0)=1

$f'\left(2\right)=3$f′(2)=3

Easy

1min

The gradient function $f'\left(x\right)$f′(x), of the function $f\left(x\right)$f(x), has been plotted on the following graph.

Easy

< 1min

Consider the four functions sketched below.

Which of the sketches match the information for $f\left(x\right)$f(x) shown in the table? Select all the correct options.

Easy

1min

sketch the graph of a function using first and second derivatives to locate stationary points and points of inflection

identify families of curves with the same derivative function