MATH 114 Midterm: MATH 114 UPenn Exam 1Midterm2

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turquoisegnu128

31 Jan 2019

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0: 9 b) 8 c) 7 d) 6 e) 4 f) 0 g) 4 h) 8, the tangent plane to the surface. 1,3,15 intersects the axis xy at : 42 , 0, find the maximum rate of change of, 24 , 12, 36 , 4 at a unique point , 6 , 44. 0z ? f x y z at the point ( 2 x y: 3, 3, 5, 2, find and classify the critical point of, 2, 6, 1, 1/2. 1 2 (cid:1) (cid:1) x cos xy dxdy. The problem can be done in the given order but if the order is switched, the integration is simpler: 0, 1, evaluate. 3 9: cos 2, 6, cos 1, 4, 2, 3 (cid:1) (cid:1) The problem can be done in the given order but if the order is switched, the integration is simpler: 0, 1.

Related Questions

1) Which of the following points does NOT reside on the graph of y^2=x+2?

A) (0,2?)

B) (?2,0)

C) (2,?2)

D) (2,2)

E) (?1,2)

2) Find x-coordinates of all points on [0,?], on the graph of the function f(x)=2sin2x?2cosx at which the tangent line is horizontal.

A) x=0,2?3,?

B) x=0,?3,?

C) x=2?3

D) x=?3

E) x=0,5?6,?

3) Use implicit differentiation to find dy/dx at the point P(2,1) for y^4+(x^2y^2)=y+4.

A) ?411

B) 4

C) 12

D) ?12

E) ?114

1) Which of the following points does NOT reside on the graph of y2=x+2?

A) (0,2?)

B) (?2,0)

C) (2,?2)

D) (2,2)

E) (?1,2)

2) Find x-coordinates of all points on [0,?], on the graph of the function f(x)=2sin2x?2cosx at which the tangent line is horizontal.

A) x=0,2?3,?

B) x=0,?3,?

C) x=2?3

D) x=?3

E) x=0,5?6,?

3) Use implicit differentiation to find dydx at the point P(2,1) for y4+x2y2=y+4.

A) ?411

B) 4

C) 12

D) ?12

E) ?114

f(x) = xe^-x^2

PLEASE SHOW WORK

a) find all critical numbers

b) find intervals that f is increasing/decreasing

c) use first derivative test for local max and min

d) apply second derivative test to f or state that it fails

e) find intervals on f for concave up and concave down

f) find all inflection points

g) Use L'Hopital's rule to find lim as x goes to infinity of f(x) and lim as x goes to -infinity of f(x)

h) find min and max value of f on interval [0,2]

i) sketch a graph of h

MATH 114 Midterm: MATH 114 UPenn Exam 1Midterm2

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