Answer:

Step-by-step explanation:
We want to find the equation of the line tangent to the graph of:

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

Simplify:

We can factor out the denominator within the square root:

Simplify:

So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:

Evaluate:

We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:

So, a point is (5/2, π/6).
Finally, by using the point-slope form, we can write:

Distribute:

Isolate. Hence, our equation is:

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Answer:
C.
If the line doesn't pass through the origin, the easiest point to pick is the origin (0,0). Substitute into your inequality.
y > 5x + 1
0 > 5(0) + 1
0 > 1 which is a false statement.
So, you shade the side of the line on which (0,0) doesn't lie.
If the statement would have be true, you shade the side of the line on which (0,0) lies.