operations with derivatives. the derivative of a constant times a function justification
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EXERCISE 1
Calculate the derivative of each of the following functions. Then find the equation of the tangent line at the indicated point.
Finding the critical points of a function y=f(x) defined by a formula
• STEP 1. Find all the points where f ‘(x)=0 or where f ‘ (x) is undefined. These are the candidates to be critical points
• STEP 2. From the candidate points choose the ones in the domain of the function f(x). Those are the critical points
Example 2
Find the critical points of the function
• Formula for y’(x)• Solve
– y’(x)=0– y’(x) undefined
• Choose the solutions which are in the domain of y(x)
Exercise 4
Each of the following functions can be represented as the product of functions f and g. Identify the functions and use the the product rule to find its derivative.
EXERCISE 5
Each of the following functions can be represented as the quotient of two functions f
and g. Clearly identify them and use the quotient rule to find its derivative. Some of
these derivatives can be calculated using previous rules as well. When it is possible you
are asked to do it.