1.7.3 Sketching the gradient function

Multiple choice

Where does $f^{'} (x)$ lie when $f (x)$ is increasing?

The straight-line gradient is

\boxed{\frac{\text{change in }y}{\text{change in }x}}

. At a particular point on a curve, its gradient is the gradient of the tangent there.

Above the horizontal axis, since $f^{'} (x) > 0$ .

It meets the horizontal axis because $f^{'} (x) = 0$ .

$f^{'} (x)$ increases.

Multiple choice

Where does $f^{'} (x)$ lie when $f (x)$ is increasing?

The straight-line gradient is

\boxed{\frac{\text{change in }y}{\text{change in }x}}

. At a particular point on a curve, its gradient is the gradient of the tangent there.

Above the horizontal axis, since $f^{'} (x) > 0$ .

It meets the horizontal axis because $f^{'} (x) = 0$ .

$f^{'} (x)$ increases.

1.7.3 Sketching the gradient function Flashcards