topic badge

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...

A

Loading Graph...

B

Loading Graph...

C

Loading Graph...

D
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
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

ACMMM112

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

ACMMM121

identify families of curves with the same derivative function

What is Mathspace

About Mathspace