(a)
We have been given an equation
. Upon taking derivative of this equation with respect to x on both the sides, we get:

(b)
In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

Therefore, equation of tangent line is:

(c)
We know that slope of tangent is given as
. The tangent will be vertical when denominator of slope is zero, that is:

When Thomas Jefferson referred to the Missouri Compromise he described it as “ fire bell in the night”. This is because he saw it as a pressing matter and he saw this as an emergency since a fire bell at night indicates that there is an emergency.
Hope this helps! :3
When considering a career, and the path to that career, it's important to take into account the average annual salary, the cost of the education, the length of the education, and the future of the industry you want to enter.
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