15.
16a.
f (x) exists on the interval a, b 1. If f (x) 0 in a, b , then f is concave upward in a, b . 2. If f (x) 0 in a, b , then f is concave downward in a, b . To locate the points of inflection of y f (x) , find the points where f (x) 0 or wher
Calculus Cheat Sheet
Trigonometric Formulas 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
sin cos 1 2 2 1 tan sec 2 1 cot csc2 sin( ) sin cos( ) cos tan( ) tan sin( A B) sin A cos B sin B cos A sin( A B) sin A cos B sin B cos A cos(A B) cos A cos B sin Asin B
30.
Definition of Arc Length If the function given by y
f (x) represents a smooth curve on the interval a, b , then the arc b 2 length of f between a and b is given by s 1 f ( x) dx . a
31. Work and Hooke's Law 1. If an object is moved a distance D