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

Application Of Derivatives

Question
CBSEENMA12035385
Wired Faculty App

Prove that the following functions do not have maxima or minima:
h(x) = x3 + x2 + x + 1

Solution

Let straight f left parenthesis straight x right parenthesis space equals space straight x cubed plus straight x squared plus straight x plus 1                            therefore space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 3 straight x squared plus 2 straight x plus 1
Now,  straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space space space space space space rightwards double arrow space space space 3 straight x squared plus 2 straight x plus 1 space equals space 0
rightwards double arrow space space space space straight x space equals space fraction numerator negative 2 plus-or-minus square root of 4 minus 12 end root over denominator 6 end fraction space equals space fraction numerator negative 2 plus-or-minus 2 square root of negative 2 end root over denominator 6 end fraction space equals space fraction numerator negative 1 plus-or-minus square root of negative 2 end root over denominator 3 end fraction
These values of x are not real.
∴    there is no real value of x for which f ' (x) = 0
∴    f (x) has neither maxima nor minima.

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