Dr. J's Maths.com
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Calculus - Differentiation - Applied max/min questions.
Type 6: Rates - Miscellaneous questions - Solutions.


 

 
  1. (i) When t = -1, height = 21.82 m.

(ii) When you take the first derivative, you see immediately this question cannot depend on calculus. You cannot silve the first derivative for t - so there is no place for a stationary point. The curve is clearly a hyperbola.

Just because it says MAXIMUM (in other cases MINIMUM) does not imply you have to use calculus.

So solve the equation to determine the value of t when H = 20 (=13.3 + 6.7).

The answer by simple algebra is t = 34.5. We cannot use the values above t = 38 because work is not permitted.
 

2. (i)

(ii) Y is the independent variable so we need to differentiate with respect to y using the quotient rule:
 

3.

 

(i)

 

(ii)

 

(iii)