Posted by Ashley on Monday, October 15, 2012 at 1:57pm.
where is f' zero or undefined?
f' = 4secθtanθ + 2sec^2 θ
so, critical numbers are where
secθ = 0 or is undefined,
2tanθ+secθ = 0 or is undefined
yes,i got 7pi/6 and 11pi/6 is that correct?
f(Ø) = 4secØ + 2tanØ
for Ø intercepts, f(Ø) = 0
4secØ + 2tanØ = 0
2/cosØ + sinØ/cosØ = 0
2 + sinØ = 0
sinØ = -2 , which is not possible
so the curve does not cross or touch the Ø axis
for y-intercept, let Ø = 0
f(0) = 4sec 0 + 2 tan 0 = 4 + 0 = 4
crosses the vertical axis at (0,4)
f ' (x) = 4 secØtanØ + 2sec^2 Ø
= 0 for max/min of f(Ø)
4/cosØ (sinØ/cosØ) = -2/cos^2 Ø
4 sinØ = -2
sinØ = -1/2
Ø = 7π/6 or Ø = 11π/6
if Ø = 7π/6 , f(7π/6) = 4(-√3/2) + 2/√3 = ....
if Ø = 11π/6, f(11π/6) = ...
I will let you finish the arithmetic
If you want the points of inflection, take the 2nd derivative, and set that equal to zero.
That will be quite a challenge.
Hmm. I was under the impression that critical numbers were numbers in the domain where f'=0 or f is not differentiable.
I think your math is great, Reiny, but maybe covers too much ground.
trig - If cosecant of theta equals 3 and cosine of theta is less than zero, find...
Trigonometry - Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 ...
Trig - Solve the following interval 0<_ (less than or equal to)0(Theta)&...
Calculus - I wanted to confirm that I solved these problems correctly (we had to...
Trigonometry - If cot 2(Theta) = 5/12 with 0 (less than or equal to) 2(Theta) (...
Calculus - Interval 4sec(theta)(sec(theta)+tan(theta))d(theta) can ...
Calculus - If cos2 theta = 1/3 and 0 is less than or equal to 2 theta and 2 ...
trig - If tan theta = sin theta, and theta is greater than or equal to 0 and ...
trig - given that 0 is less then or equal to theta and theta is less then or ...
math - find all solutions on 0 is greater than or equal to theta < 2pi ...
For Further Reading