Question 4 Consider the production function Y = ƒ (L) = e¹¹ (L² − 8) where Y = units of output, L = units of labour (a) Calculate marginal product of labour f'(L). (b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact L and Y coordinates. (c) Use the second derivatives test to classify the stationary points. (d) Find the equation of the normal to the curve at the positive L-intercept.

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Question 4
Consider the production function Y = = f(L) = e¹ (L² − 8)
where Y = units of output, L = units of labour
(a) Calculate marginal product of labour f'(L).
(b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact
L and Y coordinates.
(c) Use the second derivatives test to classify the stationary points.
(d) Find the equation of the normal to the curve at the positive L-intercept.
Transcribed Image Text:Question 4 Consider the production function Y = = f(L) = e¹ (L² − 8) where Y = units of output, L = units of labour (a) Calculate marginal product of labour f'(L). (b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact L and Y coordinates. (c) Use the second derivatives test to classify the stationary points. (d) Find the equation of the normal to the curve at the positive L-intercept.
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'' Setting f'(L) = 0:

(2L + L2 - 8) * eL = 0

To find the exact L coordinates, we need to solve the equation (2L + L2 - 8) = 0. The solutions to this quadratic equation will give us the L values for the stationary points. ''

why didn't you do a quadratic equation with the eLwhy is not (2L + L- 8 ) * e= 0

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