The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them. Note: For non-integer numerical values, you must use at least 3 decimal places. Also, you must use a 'full stop' . and not a comma ',' for a decimal point. The left-most stationary point (the one with the lower value of 𝑥 ) is located at 𝑥= Answer 1 Question 2 , 𝑦= Answer 2 Question 2 , and is a Answer 3 Question 2 The right-most stationary point (the one with the higher value of 𝑥 ) is located at 𝑥= Answer 4 Question 2 , 𝑦= Answer 5 Question 2 , and is a Answer 6 Question 2

The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them. the left-most stationary point (the one with the lower value of x) is located at x = and y = and is a point. • the right-most stationary point (the one with the higher value of x) is located at x = and y = and is a point

The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them

The function 𝑓(𝑥)=−3𝑥4+16𝑥3+24𝑥2−192𝑥+10 has critical points at some of the following 𝑥 -values. In each case identify whether the point is a critical point, and if so find out if it is a maximum, minimum or neither maximum nor minimum. The point 𝑥=−6 is Answer 1 Question 3 The point 𝑥=−2 is Answer 2 Question 3 The point 𝑥=0 is Answer 3 Question 3 The point 𝑥=2 is Answer 4 Question 3 The point 𝑥=4 is Answer 5 Question 3

For the function of two variables, f (x, y) = x3 − y2 + 9xy + 5. Find the critical points and determine their nature to complete the following sentences (making sure you use at least 3 decimal places in your answer): • the left-most stationary point (the one with the lower value of x) is located at x = and y = and is a point. • the right-most stationary point (the one with the higher value of x) is located at x = and y = and is a point

Find the 𝑥-values of both critical points of the following function. Then use the first derivative test to classify each of them as either a relative minimum, relative maximum, or neither.𝑦=−𝑥33−3𝑥22−2𝑥−7