1.) Find dy/dx, using implicit differentiation
2.)Use implicit differentiation to find the following.
a.)The slope of the tangent line at the indicated point on the graph
b.)The equation of the tangent line at the indicated point on the graph.
3.) An employment research company estimates that the value of a recent MBA graduate to an accounting company is given by the equation below, where V is the value of the graduate, e is the number of years of prior business experience, and g is the graduate school grade-point average. If V is fixed at 250 , find de/dg when g=3.1 (Round the answer to 2 decimal places.)
b.) This means that, at a value level of 230, and increase by 1.0 for a candidate with a 3.1 grade point average is worth ( ) years of experience.
- 1 decade agoFavorite Answer
1.) 將兩邊differentiate with respect to x
d[6xy-(y/6)]/dx = d[4/x]/dx
6y-(1/6)dy/dx = -4(1/x^2)
dy/dx = 36y+24/x^2
2a.) slope of tangent at (-1,2) = dy/dx at (-1,2) = m
2x^2-y^2 = xy
一樣先將兩邊diff w.r.t. x
4x-d[y^2]/dx = y
4x-(d[y^2]/dy)(dy/dx) = y (chain rule)
4x-2y(dy/dx) = y
dy/dx = (4x-y)/2y
m = (4(-1)-2)/2(2) = -3/2
2b.) 果條 tangent line (straight line)既slope係m, pass through (-1,2)
於是我地可以用中學教過既(XD) point-slope form
which is y-y1 = m(x-x1)
=> y-2 = (-3/2)(x+1)
y = (-3x+1)/2
3a.) 都係將兩邊d wrt g先, 而因為搵change of e wrt g唔關V事, 所以treat V as constant
=> 0 = (d[3e^2]/de)(de/dg)+9g^2
0 = 6e(de/dg)+9g^2
de/dg = (-9g^2)/6e
3b.) 要搵de/dg at V=230, g=3.1
(你上面寫V=250, 下面寫V=230, 我當係230先la, 如果唔係你跟step計番一次就ok)
但係我地上面計到既de/dg係in terms of g同e
=> de/dg = (-9g^2)/6e
de/dg = (-9(3.1)^2)/6(6.85) = -2.11
This means that, at a value level of 230, and increase by 1.0 for a candidate with a 3.1 grade point average is (roughly...) worth ( 2.11) years of experience.
因為當V fix死左係230, at g=3.1, 個rate of change of e wrt g係-2.11, 所以approximately when g changed by 1, e 會changed by -2.11. 亦即係話當你gpa係3.1, increase 1 gpa 可以令你少2.11 work experience 就attain到230既value level.
(for your reference: 當V fix係一個value時原本果條equation就係一條isoquant, 所以de/dg 就係所謂既 marginal rate of substitution)
step應該冇錯, 但可能會計錯, 你最好計多次 (因為我成有呢d大意野XD)
2009-02-22 06:29:05 補充：
sorry for 中英夾雜...我諗咁樣會易明d
2009-02-22 13:42:35 補充：