Question

Suppose f is a function and f(1) = 3. In addition suppose that, as x goes from 1 to 4, the average rate of change of f is – 6. In the text box below, enter the value of f(4*()). Your answer should be a number; do not enter letters or other symbols in the text box. Your answer must be exact, please do not round off your answer. For example, do not round off 1/3 to be .33. After entering your answer, click the Save Answer button.

Answer 1

f(4) = -15

Explanation:

Since we have an average rate of change, we can deduce that a line, with a gradient of -6 joins the points on the function, f, when the parameter is 1 and when it is 4, i.e. the line passes through the point (1, 3) and has a gradient of -6;

From this, we know that for every value of x we increase the, value y will decrease by 6;

So if we increase 1 by 3, to get to 4, the y value must decrease by 18 (3×6);

Written mathematically, it would look like:

f(4) = 3 + (4 - 1)(-6)

= 3 - 18

= -15

(4, -15)