What is the extreme y(θ)=tan^2(θ)-1,-pi/2 <θ< pi/2 ?

The extreme y(θ)=tan^2(θ)-1,-pi/2 <θ< pi/2 is Minimum(0,-1)

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extreme y(θ)=tan^2(θ)-1,-pi/2 <θ< pi/2

extreme points

y (θ) = tan^{2} (θ) - 1, - \frac{π}{2} < θ < \frac{π}{2}

Minimum (0, - 1)

Solution steps

Find the critical points:

θ = 0

Domain of

tan^{2} (θ) - 1, - \frac{π}{2} < θ < \frac{π}{2} : - \frac{π}{2} < θ < \frac{π}{2}

Find intervals:

Decreasing

: - \frac{π}{2} < θ < 0,

Increasing

: 0 < θ < \frac{π}{2}

Plug the extreme point

x = 0

into

tan^{2} (θ) - 1 \Rightarrow y = - 1

Minimum (0, - 1)

f (x) = 17 + 2 x - x^{2}, 0 \leq x \leq 5

f (x) = 3 x^{2} - 36 x + 24

f (x) = 9 x^{2} - 3 y^{2}

f (x) = 25 x - 50 sin (x), (- \frac{π}{4}, \frac{π}{2})

f (x, y) = - 6 x^{2} + 5 y^{2} + 12 x - 20 y - 18

What is the extreme y(θ)=tan^2(θ)-1,-pi/2 <θ< pi/2 ?
The extreme y(θ)=tan^2(θ)-1,-pi/2 <θ< pi/2 is Minimum(0,-1)