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

Jul 18, 2020

#1
+10302
+1

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

Hello Guest!

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

$$x_{Pmin}=\frac{6}{5}$$

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

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

$$y_{min}=\frac{39}{5}$$

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

!

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