Question

Use the drawing tools to form the correct answer on the number line. Function f is a quadratic function passing through the points (-4,0), (0,-12) and (3,0). Function g is modeled by the graph. Over which interval are both functions negative?

Answer 1

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing

How can we tell if a function is increasing or decreasing?

• If f′(x)>0 on an open interval, then f is increasing on the interval.
• If f′(x)<0 on an open interval, then f is decreasing on the interval.

Answer 2

ANSWER IN PICTURES.

GIVEN

. Function f is a quadratic function passing through the points (-4,0), (0,-12) and (3,0). Function g is modeled by the graph.

TO FIND

Over which interval are both functions negative.

SOLUTION

The above problem can be simply solved as follows;

To find when a function is increasing, first take the derivative, then set it equal to 0. and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing

• If f'(x)>0 on an open interval, then f is increasing on the interval. .
• If f'(x)<0 on an open interval, then f is decreasing on the interval.

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