17. Find the equation of the line that is tangent to the graph of F(x) and parallel to the given line. Function: F(x) = 2x^2 Line: 4x + y + 3 = 0

The equation of the line is .

Explanation:

Let the function be and the line be . First, we transform the equation of the line into explicit form:

(1)

By Differential Calculus, the slope at any point of the function is represented by its first derivative, that is:

(2)

If the line tangent to the function must be parallel to , then . In consequence, we clear in (2):

Then, we evaluate the function at the result found above to determine the associated value of :

By Analytical Geometry we know that an equation of the line can be formed by knowing both slope () and y-intercept (). If we know that , and , then the y-intercept of the equation of the line is:

Based on information found previously and the equation of the line, we have the equation of the line that is tanget to the graph of , so that it is parallel to is:

The equation of the line is .

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