Pre-Lab for the Hot Plate Suppose you hsve defianed a singlo-variable function J

Question

Pre-Lab for the Hot Plate Suppose you hsve defianed a singlo-variable function J and its grapl. Pick a poine (e, f(a)) on the graph. (1) What would you need to measure to determine the rate of change at this point in space? (2) What woald you snensure to determine the rate of change of J with espoct to e whem (3) Suppose that the rate of change from part (b) was 32. What does that 3.2 mean? (4) Suppose that the rate of change form part (b) was -1.4. What does that -1.4 mean? (5) The rate of change at -5 is 3.2 when s incresses to -5.2 Wh

Explanation / Answer

1) To determine rate of change we need to measure slope of curve at that point.

2) To measure rate of change at x=a

we need to measure (a) f(a) and (b) f(b) at a point b close to a

Rate of change = ( f(b) - f(a) ) / ( b-a )

3) Rate of change 3.2 means that slope at that point is positive and the function is increasing such that f increases by 3.2 units for every unit change in x.

4) Rate of change -1.4 means that the function is decreasing and slope is negative. At that point, function decreases by of 1.4 units for every unit increase in x.

5) The slope fo a curve is independent of whether we measure it towards increasing x or decreasing x. So rate of change will remain 3.2

6) Differential notation is used in calculus.

7) For x direction we can use f'(x) and for y direction we can use f'(y)

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