Inverse Fuction (1 Viewer)

[lyounamu]

http://www.boredofstudies.org/courses/maths/3u/1202628981_1990_Mathematics_Extension_1_Trial_Paper.pdf

Page 13 Q3U89-2a)!​

I got the Part 1 right but I cannot work out the 2nd part. I don't know how to "show" even though I can explain why it's like this.

Thanks in advance.

 

[conics2008]

The only reason that occurs is because for all values of x there is only one possible answer which is pi/2 =]

if f'(x)=0 then for all values of x it reache its max point

I just use defination or by graphing

 

[lyounamu]

anyone up for this question?

 

[tommykins]

Paste the question, I'm capped and CBF loading the pdf.

 

[Forbidden.]

If
f(x) = 2cos^-1(x /√ 2) - sin^-1(1 - x²), find f'(x).
Hence, or otherwise, show that:
2cos^-1(x / √2) - sin^-1(1 - x²) = π/2

Derivative is:

Spoiler

(-2√2 / √(4 - 2x²)) + (2x /√(2x² - x⁴))

 

[lolokay]

since the derivative = 0, just sub in a value for x in the original equation and whatever value you get is the value for all f(x)

for this question just sub in x=0
2cos-1(0) - sin-1(1 - 0)
= 2pi/2 - pi/2
= pi/2

 

[vafa]

The Otherwise method:

View attachment 16851