Let g(t) be a differentiable function such that g(1)=2, g(3)=4; g'(1)=1, g'(3)=1. Let f+ df denote the differential (linear) approximation of f(1.1,2.8), where f(x.y)=x?g(x²y). Let h(x,y)=3y²+6xy+2x?. Choose the TWO correct statements below. f+df=3.7 f+df =4.9 (1,1) and (1, – 1) are local extrema of h(x,y). f+df=4.5 h(x.y) has a local minimum at (1, – 1). f+df=5.2 (1,0) and (1, – 1) are local extrema of h(x,y). h(x,y) has no local minima.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.