2. The function below represents the marginal cost (in dollars per litre) for producing q litres of premium homemade cane sugar soda, where 0<9<7. S 2+ 0<9<4 f(4) = { (-3 4sa57 (b) In this part, you will use the i. Approaching from the left. Fill in the blanks: from #1 and formula for f to show that f'(4) does not exist. If q < 4, the slope of the secant line through (q, f(g)) and (4, f(4)) is 1/2 f(q) – f(4) 9-4 (You may use the graph to answer this part; you are not required to show your reasoning.) Hence, as q approaches 4 from the left, approaches 1/2

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Chapter2: Second-order Linear Odes
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2. The function below represents the marginal cost (in dollars per litre) for producing q litres of premium homemade
cane sugar soda, where 0<9<7.
f(4) = {
2+1 0sq<4
(q – 6)? 4<957
(b) In this part, you will use the idea from #1 and the formula for f to show that f'(4) does not exist.
i. Approaching from the left. Fill in the blanks:
If q < 4, the slope of the secant line through (q. f(g)) and (4, f(4) is
1/2
f(q) – f(4)
Hence, as q approaches 4 from the left,
(You may use the graph to answer this part; you are not required to show your reasoning.)
аpproaches| 1/2
9-4
ii. Approaching from the right. If q > 4, find the slope of the secant line through (4, f(4)) and (q. f(g))
f(9) – f(4)
algebraically, by finding
and simplifying. Simplify until you can easily see complete the
9-4
statement below.
f(q) – f(4)
9-4
f(a) – f(4)
Hence, as q approaches 4 from the right,
аpproaches
9-4
f(q) – f(4)
iii. Since
approaches different values
and
as q approaches 4
9-4
from the left and right respectively, we can conclude that f'(4) does not exist at q = 4.
Transcribed Image Text:2. The function below represents the marginal cost (in dollars per litre) for producing q litres of premium homemade cane sugar soda, where 0<9<7. f(4) = { 2+1 0sq<4 (q – 6)? 4<957 (b) In this part, you will use the idea from #1 and the formula for f to show that f'(4) does not exist. i. Approaching from the left. Fill in the blanks: If q < 4, the slope of the secant line through (q. f(g)) and (4, f(4) is 1/2 f(q) – f(4) Hence, as q approaches 4 from the left, (You may use the graph to answer this part; you are not required to show your reasoning.) аpproaches| 1/2 9-4 ii. Approaching from the right. If q > 4, find the slope of the secant line through (4, f(4)) and (q. f(g)) f(9) – f(4) algebraically, by finding and simplifying. Simplify until you can easily see complete the 9-4 statement below. f(q) – f(4) 9-4 f(a) – f(4) Hence, as q approaches 4 from the right, аpproaches 9-4 f(q) – f(4) iii. Since approaches different values and as q approaches 4 9-4 from the left and right respectively, we can conclude that f'(4) does not exist at q = 4.
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