# Thread: Could Someone Please Help Me With This Applied Differentiation/Integration Question

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2. ## Re: Could Someone Please Help Me With This Applied Differentiation/Integration Questi

Start by letting L = 4r. You then have a function in two unknowns. The maximum will be at points where the partial derivatives are 0 and the Hessian is negative definite, or if you can show the function is concave at that point.

3. ## Re: Could Someone Please Help Me With This Applied Differentiation/Integration Questi

Originally Posted by charlottewill
Please could somebody help me with this tutorial equation

The velocity (v) of a piston is related to the angular velocity (ω) of the crank by the relationship v = ωr{sinθ+(r/(2L))(sin2θ)} where r is length of crank and L is length of connecting rod. Find the first positive value of θ for which v is a maximum, for the case when L = 4r.

Regards,

Charlotte
$\frac{dv}{d\theta}=\omega r \cdot \left(\cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{r}{2L}\right)\right)$

$\frac{dv}{d\theta}=0 \Rightarrow \cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{r}{2L}\right)=0$

for $L=4r$ you have :

$\cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{1}{8}\right)=0$