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This lecture is from AP Calculus. Key important points are: Absolute Extrema, Principles of Algebra, Composite Equations, Interval, Critical Numbers
Typology: Exercises
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Find the absolute extrema for 𝑓(𝑥) =
3
𝑥
2
on the interval [–3, 2].
Find the critical numbers of 𝑓
4
3
4
3
= 3 sin 𝑥 + 1 ,
3
2
2 / 3
3
2
2
2
2
2
2
2
Domain: y-intercept: x-intercept(s):
Vertical asymptotes: Horizontal/Oblique asymptotes:
st
Derivative & Critical Numbers 2
nd
Derivative & Potential Points of Inflection
x f’(x) f"(x) f(x)
15. 𝑓(𝑥) = 𝑥 − cos 𝑥 , [ 0 , 4 𝜋]
Domain: y-intercept: x-intercept(s):
Vertical asymptotes: Horizontal/Oblique asymptotes:
st
Derivative & Critical Numbers 2
nd
Derivative & Potential Points of Inflection
x f’(x) f"(x) f(x)
′
2
2
′
3
2
′
′
3
2
′
′
(𝑥) = 3 cos 𝑥
′
′
2
′
′
1 / 3
′
′
2
′
′
2
2
′
2
2
3
′
2
2
′
3
