Answer:
- The instantaneous rate of increase of f(x) at
is 3. - One possible equation of this line is y = 3x - 16.
- The line is tangent to the graph of y = f(x). The slope of the line is the same as the instantaneous rate of increase of f(x) at
.
Step-by-step explanation:
<h3>1.</h3>
.
<h3>2.</h3>
.
In other words, the graph of y = f(x) passes through the point (3, -7) where
.
The point-slope form of a line in a cartesian plane is:
.
For this line,
is the point on the line, while
is the slope of the line.
The equation of this line will thus be
.
That's equivalent to
.
<h3>3.</h3>
Refer to the diagram attached. The line touches the graph of y = f(x) at x = 3 without crossing it. The line here is thus a tangent to the graph of y = f(x) at x = 3. The slope of the line represents the instantaneous rate of increase of f(x) at
.
Your answer is 39/13 miles per hour
Hope this can help you. I tried to solve each one out and I tried to write notes on how I got the equation and the answer. Message me if you can't read something, my handwriting tends to be messy :)