1. Find the first derivative of a composition of
functions.
2. Given a polynomial function , find a derivative higher
than the first or
second.
Find:
3. Given a function, find the SLOPE of the line tangent to
the function at a
given point (x,y).
Then write the equation of the tangent line in slope - intercept form .
Function: f (x) = x 3− 7x − 2 at x = 4
4. From the graph of a function , sketch by hand the
derivative of the
function. Use estimated slopes of lines tangent to the curve at specific
points.
5. Given a position function, find the velocity and
accele ration at a specific
time.
Function: f (t) = 3t3 − 40t2 +160 at t = 5
6. When will two objects have the same velocity? The same
acceleration?
7. Given the path of an object, de termine intervals of t
where the object is
advancing, retreating.
s(t) = 3t3 − 40.5t 2 +162t on [0,8]
8. Abstract application of derivative laws . No functions
given; just function
values .
Know product rule , quotient rule, derivative of a composite function.
Given:
Find:
9. Find first derivative of a sum and/or difference of trig functions . Some
chain rule involved .
10. Given the function for the path of an object,
determine intervals of t
when the object is accelerating, decelerating.
11. Find the first derivative of a sum and/or difference
of " root " functions of
x. Uses power rule with fractional exponents .
12. Find the first derivative of a composition using ln(x)
or ex.
13. Given a trig identity, use either the product or the quotient rule to derive
the derivative of the trig function.
Use the quotient rule to derive the derivative of csc(x)
14. Use the definition of the derivative to “prove” the
derivative of a
function.
To “prove” that
