Question

RogaCalcET3 14.5.003. My Notes 1 -/1 points The figure below shows the level curves of a function fx, y) and a path r ), traversed in the direction indicated. State whether the derivative frt is positive, negative, or zero at points A-D. 8 4 -10 B. 0 A 20. 30 -4 At point A the derivative is -Select At point B the derivative is-Select At point C the derivative is-Select At point D the derivative is --Select Show My Work (optiona) Submit Answer -/2 points RogaCalcET3 14.5.002. My Notes 2. Let fix, y) 3e and r(t) (, 4 + t). 1. Calculate Vf. f= 2. Calculate r(t) r(t) 3. Use the Chain Rule for Paths to calculate rE)) e) 4. Write out the composite fr(t)) as a function of t fir(E))= 5. Differentiate fr(t)) Show My Work (optionsa

Answer 1

1.

To find the sign, all we need to do is draw a tangent passing through that point and find the slope for that same.

At point A, the derivative will be 0, since the point is an intersection of two different level curves. (special case).

At point B, the derivative will be positive, since the slope of the tangent is positive.

At point C, the derivative will be positive, since the slope of the tangent is positive.

At point D, the derivative will be negative, since the slope of the tangent is negative.

2.

DOMS Patio have been j - 2639); - 0[3.89 exy O + 3 exy x - 3 [ye ay it xe xyz. g = t 3 + 14 - where + 3 = xLt) et) ļ alt det chaue lule. et ax at +2) ay 3 xexy from above- +3(414) + 3t 3 e = gt2 ye xy + 3xey Putting x= t3 4 = yet = 9tr/4+the 9 et + 3+3 et3(41) = 36 + 24 +3 +44 = 36€ 2 e 4t3 + + 4 + 12 € 3 e 4E37E4 - = 3 e ng when x=+3 a yet = 30 +3(uet) = 3e4t3+ t4 Ut3ety T wt2 4t3 3e at 34tet od elo/t) = 3e (4t37647 el + 12+3 - 362744)

Let me know, if anything needs to be explained further.