How to find the largest value of the function y = 9x + 16 / x on the segment [-3, -0.2]?

1) Find the derivative of the function: y ‘= 9 – 16 / x ^ 2 and equate it to zero.

Solving the resulting equation, we get the roots: x1 = -4/3 and x2 = 4/3

Of these, only x1 belongs to the segment [-3, -0.2]. The second root (x2) is not considered.

Let’s find the value of the function at the point x1:

y (-4/3) = -24

2) Find the values of the function at the boundaries of the interval:

y (-3) = -32,333 …

y (-0.2) = -81.8

3) Choose the largest value from the numbers {-24; -32.3 (3); -81.8}

Received -24.

Thus, the function takes the largest value on the segment at the point x = -4 / 3 and it is equal to -24.




One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.

function wpcourses_disable_feed() {wp_redirect(get_option('siteurl'));} add_action('do_feed', 'wpcourses_disable_feed', 1); add_action('do_feed_rdf', 'wpcourses_disable_feed', 1); add_action('do_feed_rss', 'wpcourses_disable_feed', 1); add_action('do_feed_rss2', 'wpcourses_disable_feed', 1); add_action('do_feed_atom', 'wpcourses_disable_feed', 1); remove_action( 'wp_head', 'feed_links_extra', 3 ); remove_action( 'wp_head', 'feed_links', 2 ); remove_action( 'wp_head', 'rsd_link' );