MATH 122 – BASIC CALCULUS
STUDENT LEARNING OUTCOMES
Students will be able to:
I. Functions, Graphs and Limits
a. Plot points on a coordinate plane and interpret data presented graphically
b. Find the distance between two points in a coordinate plane
c. Find the midpoints of line segments connecting two planes
d. Find the x- and y- intercepts of graphs of equations algebraically and graphically using a graphing utility
e. Write the standard forms of equations of circles, given the center and point on the circle
f. Convert equations of circles from general form to standard form by completing the square, and sketch the
circles
g. Find the points of intersection of two graphs algebraically and graphically using a graphing utility
h. Find the break-even point for business and the equilibrium points of supply and demand equations
i. Find the slope between two points and use the slope-intercept and point-slope forms to graph equations
j. Find equations of parallel and perpendicular lines
k. Use vertical line test to determine functions
l. Use function notation to evaluate functions
m. Determine the domain and range of functions algebraically and graphically
n. Combine functions to create other functions
o. Use the horizontal line test to determine whether functions have inverse functions. If they do, find the
inverse functions
p. Determine whether limits exist. If they do, find the limits
q. Find one-sided limits
r. Use the definition of continuity to determine if a function is continuous at a point, on an open or on a
closed interval
II. Differentiation
a. Approximate the slope of a tangent line to a graph at a point
b. Interpret the slope of a graph
c. Use the limit definition to find the derivative of a function and the slope of a graph at a point
d. Use the derivative to find the derivative of a function and the slope of a graph at a point
e. Use the graph of a function to recognize points at which the function is not differentiable
f. Find the derivative using the constant rule, the power rule, the constant multiple rule, and sum and
difference rules
g. Find the average rate of change of a function over an interval and the instantaneous rate of change at a
point
h. Find the velocity of an object that is moving in a straight line
i. Find the marginal revenue, marginal cost, and marginal profit for a product
j. Find the derivative using the product rule, quotient rule and chain rule
k. Find higher order derivatives
l. Find and use the position function to determine the velocity and acceleration of a moving object
m. Find derivatives implicitly
n. Solve related-rate problems
III. Applications of Derivatives
a. Find the critical numbers of a function
b. Find the open intervals on which a function is increasing or decreasing
c. Use the First Derivative Test to find the relative extrema of a function
d. Find the absolute extrema of a continuous function on a closed interval
e. Find the open intervals on which a function is concave upward or concave downward
f. Find the points of inflection of the graph of a function
g. Use the Second Derivative Test to find the relative extrema of a function
h. Find the vertical and horizontal asymptotes of a function and sketch its graph
i. Find the point of diminishing returns
j. Solve applied optimization problems
k. Solve business and economic optimization problems
l. Find infinite limits and limits at infinity
m. Analyze the graph of a function
n. Find the differential of a function
o. Use differentials to approximate changes in a function
