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question_answer1) Directions: (1 - 5) The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by following equation \[y=4x-\frac{1}{2}{{x}^{2}}\] where x is the number of days exposed to sunlight. The rate of growth of the plant with respect to sunlight is
question_answer2) What is the number of days it will take for the plant to grow to the maximum height?
question_answer3) What is the maximum height of the plant?
question_answer4) What will be the height of the plant after 2 days?
question_answer5) If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is
question_answer6) Directions (6 - 10) \[P(x)=-5{{x}^{2}}+125x+37500\] is the total profit function of a company, where x is the production of the company. What will be the production when the profit is maximum?
question_answer7) What will be the maximum profit?
question_answer8) Check in which interval the profit is strictly increasing.
question_answer9) When the production is 2 units what will be the profit of the company?
question_answer10) What will be production of the company when the profit is Rs 38250?
question_answer11) Directions: (11 - 15) The shape of a toy is given as \[f(x)=6(2{{x}^{4}}-{{x}^{2}}).\]To make the toy beautiful 2 sticks which are perpendicular to each other were placed at a point (2, 3), above the toy. Which value from the following may be abscissa of critical point?
question_answer12) Find the slope of the normal based on the position of the stick
question_answer13) What will be the equation of the tangent at the critical point if it passes through (2, 3)?
question_answer14) Find the second order derivative of the function at x =5.
question_answer15) At which of the following intervals will \[f\text{ }\left( x \right)\]be strictly increasing?
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