ntshomo37
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

at what value of x, the function 2x^3/3+2x^2-6x+4 is minimum​

Sagot :

lublana

Answer:

x=1

Step-by-step explanation:

We are given that

[tex]\frac{2x^3}{3}+2x^2-6x+4[/tex]

We have to find the value of x for which function is minimum.

Differentiate w.r.t x

[tex]f'(x)=2x^2+4x-6[/tex]

Substitute f'(x)=0

[tex]2x^2+4x-6=0[/tex]

[tex]x^2+2x-3=0[/tex]

[tex]x^2+3x-x-3=0[/tex]

[tex]x(x+3)-1(x+3)=0[/tex]

[tex](x-1)(x+3)=0[/tex]

[tex]x=1,-3[/tex]

Again, differentiate w.r.t x

[tex]f''(x)=4x+4[/tex]

[tex]f''(1)=4(1)+4=8>0[/tex]

[tex]f''(-3)=4(-3)+4=-8<0[/tex]

Hence, the function is minimum at x=1

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.