TRUE OR FALSE

{ll If fix} has a minimum at x=a. then there exists an a, such that fix} :- f[a]l for even,r x in [a- a, a+ a}. {2] If f'lx}=g'[x]l then f{x]=g{x} +c, where c is a constant. {3] If x=c is an inflection point for f, then flc} must be a local maximum or local minimum for f. {4] _ f[x]| = ax2 +bx +c. [with a at D}. can have onlv one critical point. {5] _The Second Shape Theorem is exactlv the converse of the First Shape Theorem. {6] _ If fix} has an extreme value at x=a then f is differentiable at x=a. {Tl _ If f'lc] =42} then f has either a minimum or maximum at x=c. {S} Iff is continuous in an open interval la, b} then f attains maximum or minimum in (a, b}. {9] _ If a differentiable function f has a minimum or maximum at x=c. then f'{c1=D. {10] An extreme value of function can only.r occur at a critical number. {11] Iff is a continuous function on a closed interval [a, b], then fattains both max and min values on [a, b]. {12] lfvou averaged SD milesfhr. during a trip then at some instant during the trip, vou were travelling exactlv at 312} milesj'hr. {13] (La, f[x}l is nite for anvx in [a, b]}. {14] whether f is curving upward or downward. {15] If f is continuous on a closed interval [a, b], then the function fis bounded The second derivative of a function f will tell us about the "concavity" of f, The mean value theorem applies as long as the function is continuous in an interval [a, b]