Explanation Given: The equation of parabola is y = a x 2 + b x + c . Approach: The first derivative is zeros or undefined at vertex of the parabola. Calculation: Consider the given function: y = a x 2 + b x + c Differentiate the above function with respect to x : y ′ ( x ) = d d x ( a x 2 + b x + c ) = d d x ( a x 2 ) + d d x ( b x ) + d d x ( c ) = 2 a x + b The first derivative is zeros or undefined at vertex of the parabola. 2 a x + b = 0 Solve for x : x = − b 2 a Substitute − b 2 a for x in the equation y ( x ) = a x 2 + b x + c

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 5.2, Problem 38E

To determine

To find:

The vertex of each parabola y=ax2+bx+c with help of derivative.

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Chapter 5.2, Problem 37E

Chapter 5.2, Problem 39E

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 5.1 - YOUR TURN Find where the function is increasing...Ch. 5.1 - YOUR TURN 2 Find the intervals in which...Ch. 5.1 - Prob. 3YT Ch. 5.1 - YOUR TURN Find where f is increasing and...Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Find the open intervals where the functions...Ch. 5.1 - Prob. 6E

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