Answer: 3/10
Step-by-step explanation:
Take the derivative of [tex]10x^2-6x-3[/tex] to get [tex]20x-6[/tex]. Set that equal to 0 to find the critical points of the function. The critical points is when the slope is either 0 or undefined.
Now do:
[tex]20x-6=0\\20x=6\\x=\frac{6}{20} = \frac{3}{10}[/tex]
There are quite a few more steps to actually find the minimum, but for this example you can automatically assume its a minimum because it is the only critical point of the function. Ill show you these extra steps tho.
Plug in two numbers into the derivative. One that is less than 3/10 and one that is greater than 3/10. The numbers 0 and 1 are fine. When x = 0, the function is -6. When x = 1, the function is +14. A switch from negative to positive indicates a minimum value
