Search & Filtering
Given the function f(x,y) = e^x ( x^2 - y^2) find all critical points and classify each as a local maximum, local minimum, or neither.
Find the absolute maximum and minimum values of the function f(x,y) = x + y - xy
on the closed triangular region with vertices (0,0), (0,2), and (4,0).
Given the function f(x,y)= arctan(xy) (A) Find the gradient vector f(x,y) (B) Compute the directional derivative of f at the point (1,2) in the direction of the vector
v = 5i + 10j
“The series expansion of the function cosx in powers of x contains all even
powers of x only.” True/ False ?
Find acute angle between intersecting curves. Write normal line, tangent line for each curves at the intersec tion point.
y = x ^ 3 , x = y ^ 2
The perimeter of an isosceles triangle is 28cm. What is the maximum area possible?
The perimeter of an isosceles triangle is 28cm. What is the maximum area possible?
Graph each function. Then identify the vertex, two points, domain, and range.
f(x) = |-1/5(x + 5)| + 2
square as a function of the length of its diagonal.
20. Suppose the average family spends 25% of its income I on food F, and 10% of this amount
F is spent on junk food J. Write J as a function of I.
21. Cliff left point A at 8 A.M. walking east at 3 kph. Renz left point A at 9 A.M. walking north
at 4 kph.
(a) Express the distance between Cliff and Renz as a function of the elapsed time
thereafter. Show that distance travelled is a function of time and find the rule of the
function.
12. A man jogs for 20 minutes at a rate of 6 kph, then walks for 30 minutes at a rate of 3 kph,
then sits and rests for 15 minutes and finally walks for 45 minutes. Find the rule of the
function that expresses his distance travelled as a function of time
