Answer to Question #250066 in Electrical Engineering for Nazi

Question #250066
Find the critical point of the following problems
a. F(x)=8-3x+x^2
b. F(x)=x^4-18x^2+9
c. F(x)=x^3-5x^2-8x+3
d. F(x)= x^2/(x^2+1)
e F(x)=x^2/(x^2-1)
f F(x)=(x^2-1)^3
1
Expert's answer
2021-10-13T04:57:37-0400

a)

"F(x)=8-3x+x^2\\\\\nF'(x)=-3+2x\\\\\n\\text{At critical point, derivative is 0}\\\\\n-3+2x=0\\\\\n2x=3\\\\\nx=1.5\\\\\nF(x)=8-3(1.5)+(1.5)^2=5.75\\\\\n\\text{Critical point is (1.5,5.75)}"

b)

"F(x)=x^4-18x^2+9\\\\\nF'(x)=4x^3-36x\\\\\n4x^3-36x=0\\\\\nx=0,3\\\\\n\\text{at x=0, F(x)=9}\\\\\n\\text{at x=3, F(x)=-72}\\\\\n\\text{Critical points are (0,9) and (3,-72)}"

c)

"F(x)=x^3-5x^2-8x+3\\\\\nF'(x)=3x^2-10x-8\\\\\n3x^2-10x-8=0\\\\\nx=4,\\frac{-2}{3}\\\\\n\\text{At x=4, F(x)=-2}\\\\\n\\text{At x=}\\frac{-2}{3}\\text{ F(x)=}\\frac{157}{27}\\\\\n\\text{Critical points are (4,-2) and } (\\frac{-2}3,\\frac{157}{27})\\\\\nd)\\\\\nF(x)=\\dfrac{x^2}{x^2+1}\\\\\n\\text{has no critical point}\\\\\ne)F(x)=\\dfrac{x^2}{x^2-1}\\\\\n\\text{has no critical point}\\\\\nf) F(x)=(x^2-1)^3\\\\\nF'(x)=2x(x^2-1)^2\\\\\n2x(x^2-1)^2=0\\\\\nx=0,-1,1\\\\\n\\text{critical points are (0,-1),(-1,0) and (1,0)}"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS