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Derivatives : Product and Quotient Rules

1. For the following function find the value of the derivative at the specific point given using:
- the definition of the derivative
- the sum rule for derivatives

Show that both methods lead to the same result.
f(x)=-x3+3x2-2 at x=1

2. Find an equation to the tangent at the given point, using the Product Rule and then the Quotient Rule when determining the derivative.

Show the both these methods result in the same solution.
y= 2+x at the point (1,-3)

See attached file for full problem description.

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Solution Summary

Derivatives, product and quotient rules are investigated.The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.