Practice Application Of Derivatives (3.6) - Calculus

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9 questions

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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the equation of the tangent line at a point P(x₁, y₁) if the slope is m?
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Use the point-slope form of the linear equation.
Question 2.
True or False: The slope of the normal line is the negative reciprocal of the slope of the tangent line.
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Recall the relationship between perpendicular slopes.
3Question 3.
What does the derivative represent?
- The area under a curve
- The rate of change at a point
- The maximum value of a function
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Think about how we perceive change in motion.
4Question 4.
True or False: A point is a local maximum if the first derivative is zero and the second derivative is positive.
- True
- False
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Remember the conditions for maximum and minimum.
Question 5.
A rectangular garden has dimensions x and y. The area A = xy = 100. Express y in terms of x and find dimensions that minimize the perimeter.
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Optimize the perimeter as a function of area.
Question 6.
A company's cost function is C(x) = x³ - 5x² + 8x + 15. Determine the number of units produced for minimized cost.
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Use both derivatives to confirm minimum value.

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