ntshomo37
Answered

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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

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