The value of 2 in 204.75 is how many times in the value of the 2 in 103.52
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Over this 10-minute interval, the car's average acceleration is
The MVT says that at some point during this 10-minute interval, the car must have had an acceleration of 60 mi/h^2.
We have the following curve:
So we need to find <span>an equation of the tangent line to this curve at the point
. So let's find out if this point, in fact, belongs to the curve:
</span>
.
<span>
We also know that:
</span>
<span>
Given that the point is:
</span>
Then we will say that:
Therefore:
Computing the derivative:
So the derivative solved for
is in fact the slope of the line at the point , then:
Finally, the tangent line is:
<em>This is shown in the figure below.</em><span>
</span>
So we need to find <span>an equation of the tangent line to this curve at the point
</span>
<span>
We also know that:
</span>
Given that the point is:
</span>
Then we will say that:
Therefore:
Computing the derivative:
So the derivative solved for
Finally, the tangent line is:
<em>This is shown in the figure below.</em><span>
</span>