Trig function question help needed (1 Viewer)

[john1464]

Using calculus. sketch the graph of y=cosx(1 +sinx) for 0>x>2pie (the ">" are greater than or equal)

 

[Librah]

Using calculus. sketch the graph of y=cosx(1 +sinx) for 0>x>2pie (the ">" are greater than or equal)

0>2pi????

 

[john1464]

sorry its the wrong way round should be <

 

[Kaido]

Use product rule. Let u=cosx, v=1+sinx
Find turning/inflection points (may need to differentiate twice)
Slot a few key values e.g. 0, pi, 2pi if you are unsure

 

[john1464]

Do i need to find the stationary points?

 

[Silly Sausage]

Yes

Differentiate w/th product rule
dy/dx=0; solve for x
substitute into original function for y value for max/min
d^2y/dx^2=0
substitute into original function for y value for inflection pts
sketch function

 

[john1464]

I cant seem to solve for x after the first derivative

 

[Silly Sausage]

Did you get

 

[john1464]

yes but i dont know where to go from there

 

[InteGrand]

Using calculus. sketch the graph of y=cosx(1 +sinx) for 0>x>2pie (the ">" are greater than or equal)

using the product rule.

i.e.

(since )

Set the derivative to 0 for stationary points, then .

This is a quadratic in sin x, which can be factorised:







Now you can find the appropriate values of x for the stationary points.

 

[Silly Sausage]

^^^
For second derivative, you need the product rule. You should get something like this:

 

[john1464]

Thank you everyone much appreciated