Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x³ + 3x² y − y³ − 15x.

a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square).

b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the square.

Expert Solution

Colby Messinger answered 1 year ago

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and...

Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and (3,3) are stationary points of f and classify these points as maximum, minimum or saddle point. Obtain the maximum or minimum value of f.

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to...

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to calculate the critical points and all local minima, local maxima and saddle points. How should this be done?

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and...

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and fye(x, y). b) Find all critical points of f(x, y). c) Classify the critical points of f(x, y) (as local max, local min, saddle). 2.Consider f(x) = 2x-x2and g(x) = x2 a) [2 points] Find the intersection points (if any) of the graphs of f(x) and g(x). b) [4 points] Graph the functions f(x) and g(x), and shade the region bounded by: f(x), g(x),...

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1, −2) and a = <3, −5>. This problem has five parts. (a) [5 pts.] Find the first partial derivatives of f(x, y). (b) [5 pts.] Find all of the second-order partial derivatives of f(x, y). (c) [5 pts.] Find an equation of the tangent plane to f(x, y) at P. (d) [5 pts.] Find ∇f. (This is still part of number 8) (e)Find the...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find...

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find the intervals where f is increasing, and decreasing. (b) Find the intervals where f is concave up, and concave down. (c) Find the local maxima, the local minima, and the inflection points. (d) Find the Maximum and Minimum Absolute of f over [−2, 2].

Question

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Solutions

Expert Solution

Related Solutions

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and...

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to...

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and...

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find...

Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>=...

Find and classify the local extrema of the function f(x,y) = (x^3)y+12(x^2)+16(y^2).

Find the arclength of y=3x3/2 on 1≤x≤2