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17.3: Applications of Second-Order Differential Equations

Applications of Derivatives in Maths and in Real Life (With Examples)

Second Derivative | Definition, Formula & Examples

Derivative Notation Overview & Uses

SOLVED: Suppose that f= 123A) Use interval notation to indicate where f is defined. If it is defined on more than one interval, enter the union of all intervals where f is defined. Domain: Find all intercepts. If there are no intercepts, enter None. If there are more than one, enter them separated by commas. x-intercept(s)= y-intercept(s)=C Find all critical values of f. If there are no critical values, enter None. If there are more than one, enter them separated by commas. Critical value(s)=D U

SOLVED: In Exercises 7-23, find the critical points of the function. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails). f(x, y)=(x-y) e^x^2-y^2 | Numerade

Find the relative extrema, if any, of each function. Use the Second Derivative Test if applicable. f(x)=(2 x)/(x^2+1) | Numerade

Given: f(x,y) = ky^2 – 2y^3 – kx^3 2kxy.A. Given that the function f(x,y) has a critical point at (0,0), use a second derivative test to explain why the function f has a saddle point at (0,0) for all nonzero values of k. Show ALL work.B. Given that the function f(x,y) has a critical point at (2/3,2/3) when k = 1, use a second derivative test to determine whether (2/3,2/3) is a local maximum, local minimum, or saddle point, or determine whether a second derivative test is inconclusive. Show