Derivatives + Finding Unknown Values

[Chrizzle]

Sorted.

 

[tkhunny]

You probably should start with finding four derivatives. Let's see what you get.

 

[Chrizzle]

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[Deleted member 4993]

f(x)=asin(x)+bx³ <<<< is it x² or x³
f'(x)=acos(x)+3bx²

f''(x)=-asin(x)+6bx

f'''(x)=-acos(x)+6b

f^(iv)(x)=asin(x)+6b >>>>> that 6b should not be there

Are these correct? What do we do next?

After correcting it, start putting the conditions. You wou would get twoequations for two unknowns (a & b) → solve.

First condition:

f'(π) = 2 → a * π + 3bπ² = 2 ..... and continue.....

 

[Chrizzle]

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[Deleted member 4993]

<sup>Ohhh and....

It's f(x)=asin(x)+bx^2 ​...sorry about that</sup>
Which means all the derivatives change a little bit from what I had before.

f(x)=asin(x)+bx²
f'(x)=acos(x)+2bx
f''(x)=-asin(x)+2b
f'''(x)=-acos(x)
f^(iv)(x)=asin(x)

Are these correct now? .....................Yes

That was \(\displaystyle \pi\) or "pi" not "n"

 

[Chrizzle]

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[Chrizzle]

Any idea?

 

[HallsofIvy]

Oh, c'mon. \(\displaystyle (a sin(x))^2+ (a cos(x))^2= a^2(sin^2(x)+ cos^2(x))= 2\).

Do you know what \(\displaystyle sin^2(x)+ cos^2(x)\) is?