MATH 121 – Test #2 Study Guide Section 2.3 constant rule

MATH 121 – Test #2 Study Guide
Section 2.3
 know and use the constant rule, power rule, constant multiple rule, sum rule and
difference rules
Section 2.4
 know and use the product rule and quotient rule
 know and use derivative formulas for all six trig functions (p. 111)
 prove the derivative formulas for tan x and sec x
Section 2.5
 know and use the chain rule (need to be able to use this in combination with all the
previous rules from Sections 2.3 and 2.4)
 knowing the chain rule for powers (p. 116) will help save time
Section 2.6
 use implicit differentiation to find dy/dx when the relationship between y and x is not
given in explicit form (for example, x2 + xy + y2 = 10 ) and find the slope at a given
point (x,y)
Section 2.7
 set up and solve related rates problems such as on p. 131.
Section 2.8
 construct the linearization L(x) of f(x) at a point x=a
 use the linearization to estimate f(x) near x=a
 given y written as a function of x compute the differential dy
 use dy to estimate the change (or error) in y caused by a small change (or error) in x
Section 3.1
 know the definition of absolute and local minimum and maximum
 identify the critical numbers of a function
 locate all absolute and local minima and maxima of a continuous function f(x) on a
closed interval [a,b]