DIFFERENTIAL CALCULUS EXAM QUESTIONS AND ANSWERS

DIFFERENTIAL CALCULUS EXAM
QUESTIONS AND ANSWERS
d/dx e^x - ANSWER-e^x

Velocity - ANSWER-Derivative of position

Acceleration - ANSWER-Derivative of velocity

Extreme values occur where - ANSWER-The derivative is 0, undefined, or at the
endpoints

Max - ANSWER-Derivative is 0 and changes sign from positive to negative

Min - ANSWER-Derivative is 0 and changes sign from negative to positive

Absolute extreme values - ANSWER-Global extreme values

Local extreme values - ANSWER-Relative extreme values

Max or min value - ANSWER-'y' value

Increasing - ANSWER-Derivative is positive

Decreasing - ANSWER-Derivative is negative

Concave up - ANSWER-2nd derivative is positive

Concave down - ANSWER-2nd derivative is negative

Point of Inflection - ANSWER-2nd derivative is 0 or undefined and changes sign

Optimization - ANSWER-Finding max and min in real life

Related Rates - ANSWER-Finding how fast something is changing in real life

Linearization of a curve - ANSWER-L(x) = f(a) - f'(a)(x-a)
Average Rate of Change - ANSWER-Slope of two points

Instantaneous Rate of Change - ANSWER-Derivative

Derivative is - ANSWER-the slope of the tangent line at one point