+91-8076753736[email protected]
logo
logo
-->

Application Of Derivatives

Question
CBSEENMA12035355
Wired Faculty App

The interval in which y = x2e–x is increasing is

  • (– ∞, ∞)
  • (– 2,  0)
  • (2, ∞)
  • (0,  2)

Solution

D.

(0,  2)

Here,    straight y space equals space straight x squared straight e to the power of negative straight x end exponent
therefore space space space space space dy over dx space equals space straight x squared straight d over dx left parenthesis straight e to the power of negative straight x end exponent right parenthesis space plus space straight e to the power of negative straight x end exponent straight d over dx left parenthesis straight x squared right parenthesis space equals space straight x squared. space straight e to the power of negative straight x end exponent straight d over dx left parenthesis negative straight x right parenthesis space plus straight e to the power of negative straight x end exponent. space 2 straight x
                  <pre>uncaught exception: <b>Http Error #404</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 61<br />#0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #404') #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('com_wiris_plugi...', Array) #2 [internal function]: _hx_lambda->execute('Http Error #404') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array) #4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #404') #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('haxe_Http_5', Array) #6 [internal function]: _hx_lambda->execute('Http Error #404') #7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array) #8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #404') #9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL) #10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true) #11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true) #12 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #13 {main}</pre>
For y to be increasing, 
                        dy over dx greater than 0 space space space space space space space space space space space rightwards double arrow space space space minus straight x left parenthesis straight x minus 2 right parenthesis thin space straight e to the power of negative straight x end exponent greater than 0 space space space space rightwards double arrow space space space straight x left parenthesis straight x minus 2 right parenthesis space less than space 0 space space space rightwards double arrow space space space straight x space element of space space left parenthesis 0 comma space 2 right parenthesis
therefore space space space left parenthesis straight D right parenthesis space is space correct space answer.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation