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Popular Calculus >

f(x)=4sec^2(x)

Solution

f (x) = 4 sec^{2} (x)

Solution

Period : π

Domain : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range : f (x) \geq 4

Y Intercepts : (0, 4)

Asymptotes : Vertical x = \frac{π}{2} + πn

Extreme Points : Minimum (πn, 4)

+1

Interval Notation

Domain : [πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Range : [4, \infty)

Solution steps

Periodicity of

4 sec^{2} (x) : π

Domain of

4 sec^{2} (x) : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range of

4 sec^{2} (x) : f (x) \geq 4

Axis interception points of

4 sec^{2} (x) :

Y Intercepts

: (0, 4)

Asymptotes of

4 sec^{2} (x) :

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

4 sec^{2} (x) :

Minimum

(πn, 4)

Graph

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