Question

find maximum & minimum value of y = x3 - 15÷2 x2 + 18x​

Answer 1

Answer:

The maximum & minimum values of  $y=x^3-\frac{15}{2} x^{2} +18x$ are 13.5 and -148.5

Step-by-step explanation:

• The maximum and the minimum value of the function are determined with the use of the differential equation.
• The function is given as

       $y=x^3-\frac{15}{2} x^{2} +18x$

• Differentiate the function w.r.t  x

      $\frac{dy}{dx} =3x^{2} -15x+18$

• Put $\frac{dy}{dx} =0$

       $3x^{2} -15x+18=0\\x^{2} -5x+6=0\\(x-3)(x-2)=0\\x=2,x=3$

• Again differentiate the function w.r.t x

      $\frac{d^2y}{dx^2} =6x-15$

• Put the value of x in double derivative to find maxima and minima
• if x =2, $\frac{d^2y}{dx^2}=-3$ maxima occurs
• if x=3, $\frac{d^2y}{dx^2}=3$  minima occur.
• To find the minimum and maximum value of the function, put the value of x.

     $y=13.5 \ at \ x=3\\y=-148.5 \ at \ x=-3$