gallentlyspeaking
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- Dec 1, 2016
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help finding info about a function without knowing the actual function? (AP Calc AB)
given that f is continuous on [-2,5] and...
f(-2)=10
f(5)=6
f'(x) is positive on (-2. 1) and (3,5); negative on (1,3); 0 at x=1 and undefined at x=3
f''(x) is positive on (3, 5), negative on (-2, 1) and (1,3); 0 at x=0. and undefined at x=3
a)find intervals where f is increasing or decreasing
b) find where f has absolute extrema
c) find where f has points of inflection
d) find intervals where f is concave up and concave down
i tried working through it & got..
a) I: [2,-1] and (3,5] D: [1,3) (not sure about use of brackets vs parenthesis with the 3 since it's undefined??)
b) x=1 max, x=3 min based on my rough sketch of the graph..
c) IP at x=3? can this occur at an undefined???
d)cc up on (3, 5) cc down on (-2, 3).. but should the interval be more precise? is (3, 5) concave up??
please correct/guide me.. I really want to understand this for the AP exam!!!
given that f is continuous on [-2,5] and...
f(-2)=10
f(5)=6
f'(x) is positive on (-2. 1) and (3,5); negative on (1,3); 0 at x=1 and undefined at x=3
f''(x) is positive on (3, 5), negative on (-2, 1) and (1,3); 0 at x=0. and undefined at x=3
a)find intervals where f is increasing or decreasing
b) find where f has absolute extrema
c) find where f has points of inflection
d) find intervals where f is concave up and concave down
i tried working through it & got..
a) I: [2,-1] and (3,5] D: [1,3) (not sure about use of brackets vs parenthesis with the 3 since it's undefined??)
b) x=1 max, x=3 min based on my rough sketch of the graph..
c) IP at x=3? can this occur at an undefined???
d)cc up on (3, 5) cc down on (-2, 3).. but should the interval be more precise? is (3, 5) concave up??
please correct/guide me.. I really want to understand this for the AP exam!!!
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