+0  
 
0
96
2
avatar

Find the minimum value of y = 5x^2 - 12x + 15.

 Jul 18, 2020
 #1
avatar+10302 
+1

Find the minimum value of y = 5x^2 - 12x + 15.

 

Hello Guest!

 

\( y = 5x^2 - 12x + 15\\ \frac{dy}{dx}=10x-12=0\\ x_{min}=\frac{12}{10}\)

\(x_{Pmin}=\frac{6}{5}\)

\(y_{min}=5\cdot \frac{36}{25}-12\cdot \frac{6}{5}+15\)

\(y_{min}=\frac{5\cdot 36-12\cdot6\cdot 5+15\cdot 25}{25}=\frac{195}{25}\)

\(y_{min}=\frac{39}{5}\)

 

\(P_{min}(1.2,7.8)\)

laugh  !

 Jul 18, 2020
edited by asinus  Jul 18, 2020
edited by asinus  Jul 18, 2020
 #2
avatar+27605 
+2

If you are not in calculus, you may not know how to do the deriviative of the function.

This is a bowl shaped parabola (because the leading coefficient is positive)

   the minumum value of the fiunction will occur at an 'x' value of   - b/2a  

        where  b =  -12    and   a = 5

    Use THIS 'x' value in the equation to calculate the minumum value ('y') of the function.....

 Jul 18, 2020

55 Online Users

avatar