Find dy/dx for a & b
a) sin x+cos y=1
b) cos x^2 = xe^y
c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the
second derivative f'' (x) equals zero.
d) For what value of the constant c is the function f continuous
on (−∞,∞)?
f(x) = {cx^2 + 2x, x < 2 ,
2x + 4, x ≥ 2}
dx dt =ax+by dy dt =−x − y,
2. As the values of a and b are changed so that the point (a,b)
moves from one region to another, the type of the linear system
changes, that is, a bifurcation occurs. Which of these bifurcations
is important for the long-term behavior of solutions? Which of
these bifurcations corresponds to a dramatic change in the phase
plane or the x(t)and y(t)-graphs?
Consider the curve given by the equation y^2 - 2x^2y = 3
a) Find dy/dx.
b) Write an equation for the line tangent to the curve at the
point (1, -1).
c) Find the coordinates of all points on the curve at which the
line tangent to the curve at that point is horizontal. d) Evaluate
d 2y /dx2 at the point (1, -1).