MATH& 151 Calculus I

• Describe a function verbally, algebraically, graphically, and numerically
• Define and calculate limits
• Define the derivative of a function
• Interpret derivatives as slopes of tangent lines and rates of change
• Differentiate polynomial, exponential, logarithmic, and trigonometric functions
• Apply the product, quotient, and chain rules to differentiate functions
• Use implicit differentiation
• Graph functions and their derivatives
• Use linear approximation to estimate the value of a function
• Calculate the maximum and minimum values of a function
• Apply L’Hospital’s rule for solving indeterminate forms
• Approximate solutions using curve sketching
• Define antiderivative and find the antiderivative of a function
• Solve application problems using differential calculus
• Use problem solving skills, pattern recognition, substitution, structural rules, and quantitative modeling to solve problems involving differential calculus and limits