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Applications of the Derivative

Please see the attached file for the fully formatted problems.

For the function y= sq root (x2 - 9)
(i) Find the slope of the tangent line to the function at the point (5, 4).
(ii) Find the equation of the normal line at the point (5, 4).

2. A ladder 10 m long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at 2 m/s. How fast is the top sliding down the wall when the foot of the ladder is 6m from the wall?

3. (a) For the function y = 2x3 + 6, find:
(i) the x- and y- intercepts.
(ii) the maxima, minima and any points of inflection
(iii) the values of x where the function is concave up and concave down.
(b) Use your answers to part (a) to draw a sketch graph of the function y=2x3+6 for?3 x 4.

4. An analyst has found that a company's total revenue is given by
R(q)= 1200q ? 3q2 where q units are demanded per week. Find the level of production that will maximize the company's total revenue and then determine this revenue.
On the same set of axes, sketch the cues of the function y = 8/(x2 + 4) and its first derivative.
Make at least five (5) comments on how the y-coordinates of the derivative curve are related to the slope of the original curve.