 Hi and welcome to the session. Let us discuss the following question. Question says, prove that the following functions do not have maxima or minima. Function h is given by hx is equal to xq plus x square plus x plus 1. Let us start with the solution now. We are given hx is equal to xq plus x square plus 1. Now differentiating both sides with respect to x, we get h dash x is equal to 3x square plus 2x plus 1 plus 0. Derivative of xq is 3x square, derivative of x square is 2x and derivative of x is 1. Derivative of 1 is 0. Now we can write h dash x is equal to 3x square plus 2x plus 1. Let us find out all the points at which h dash x is equal to 0. So now we will put h dash x equal to 0. We get 3x square plus 2x plus 1 is equal to 0. Now this implies x is equal to minus 2 plus minus square root of 4 minus 4 multiplied by 3 multiplied by 1 upon 2 multiplied by 3. Let us recall if we are given an equation ax square plus bx plus c is equal to 0 then x is given by minus p plus minus under root b square minus 4ac upon 2a. Simplifying this expression we get x is equal to minus 2 plus minus square root of minus 8 upon 6. Now this implies x has imaginary values. Now we get for any real value of x, h dash x is not equal to 0. So our required answer is hx equal to xq plus x square plus x plus 1 does not have maxima or minima. This completes the session. Hope you understood the session. Take care and have a nice day.