Concept explainers
a)
To determine slope of the parabola at each of the points where it crosses the coordinate axes vertically.
a)
Answer to Problem 74RE
Slope of parabola where tangent line is vertical is infinity
Explanation of Solution
Given: Equation of parabola
Concept Used: Differentiation with respect to
Calculation: We have equation
Differentiate above equation with respect to
Tangent will be vertical when denominator of the derivative equals to 0
Put
Now put
Hence, the point where the tangent line is vertical is
Now we find the slope of parabola by putting point
Conclusion: Slope of parabola where tangent line is vertical is infinity
b)
To determine slope of the parabola at each of the points where it crosses the coordinate axes horizontally.
b)
Answer to Problem 74RE
Slope of parabola where tangent line is horizontal is
Explanation of Solution
Given: Equation of parabola
Concept Used: Differentiation with respect to
Calculation: We have equation
Differentiate above equation with respect to
Tangent will be horizontal when numerator of
Now, substitute the
Now put
Hence, the point where the tangent is horizontal is
Now we find the slope of parabola by putting point
Conclusion: Slope of parabola where tangent line is horizontal is
Chapter 4 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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