2015 TWO(c)

Merit

Question

The graph below shows the function

y = f(x)

.

Loading diagram...

For the function above:

(i) Find the value(s) of

x

that meet the following conditions:

1.

f(x)

is not defined:

2.

f(x)

is not differentiable:

3.

f''(x) > 0

:

(ii) What is the value of

f(-1)

?

State clearly if the value does not exist.

(iii) What is the value of

\lim_{x\to2} f(x)

?

State clearly if the value does not exist.

Official Answer

1.

x=1

2.

x=-1, 1, 2

3.

-1<x<1

(ii)

3

(iii)
Does not exist.

Grading Criteria

Achievement (u)

Two correct answers.

Merit (r)

Four correct answers.

Excellence T1

-

Excellence T2

-

Exam Paper (2015)Assessment Schedule (2015)

Related Questions

2024 THREE(c)Merit

Find the $x$-value(s) of any stationary point(s) on the graph of the function $f(x)=\dfrac{x^2-5x+4...

2024 THREE(d)Merit

Jamie is doing some baking and pouring the flour to form a conical pile. The height o...

2024 THREE(b)Achievement

The graph below shows the function $y = f(x)$. [DIAGRAM] (i) For the function above, find the valu...

2024 TWO(c)Merit

Show that $y = \sin(x^2) - \cos(x)$ is a solution to the equation $\dfrac{d^2y}{dx^2} + 4x^2\,y = 2...

2024 ONE(d)Merit

Find the $x$-value(s) of any stationary points on the graph of the function below, and determine the...