# Science:Math Exam Resources/Courses/MATH200/April 2012/Question 03

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MATH200 April 2012
Other MATH200 Exams

### Question 03

Let ${\displaystyle \displaystyle z=f(x,y)}$, where ${\displaystyle \displaystyle f(x,y)}$ has continuous second order partial derivatives, and

{\displaystyle {\begin{aligned}x&=2t^{2},&y&=t^{3},&&\\f_{x}(2,1)&=5,&f_{y}(2,1)&=-2,&&\\f_{xx}(2,1)&=2,&f_{xy}(2,1)&=1,&f_{yy}(2,1)&=-4\end{aligned}}}

Find ${\displaystyle {\frac {{\textrm {d}}^{2}z}{{\textrm {d}}t^{2}}}}$ when t=1.

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