${ message }
Your cart is empty
Discount (${discount_percentage}%) : - ${discount}KD
Need Help?
How was the speed of the video ?
How well did you understood the video ?
Was the video helpful?
Was the notes helpful?
Sign up to try our free practice
KD
15.500
1 month
Add to cart
34.500
4 months
Subscribe to Calculus A
Practice (Free)
Practice
Given $$\longrightarrow X Y=100 \quad x>0 \quad Y>0$$
$$f=x+y \quad$$ but $$\quad y=\frac{100}{x}$$
$$f=x+\frac{100}{x} \longrightarrow f^{\prime}(x)=1-\frac{100}{x^{2}} \rightarrow f^{\prime}(x)=\frac{x^{2}-100}{x^{2}}$$
$$f^{\prime}(x)=0 \longrightarrow \frac{x^{2}-100}{x^{2}}=0 \rightarrow x^{2}-100=0 \rightarrow(x+10)(x-10)=0$$
$$x=10, x=-10$$ rejected
$$x=10$$
Applying Second Derivative Test:
$$f^{\prime \prime}(x)=\frac{-100 (2 x)(-1)}{x^{4}}=\frac{200}{x^{3}}$$
$$f^{\prime \prime}(10)=\frac{200}{1000}>0$$
\ F has Iocal minimum at $$x=10$$
$$y=\frac{100}{x}=\frac{100}{10}=10$$
$$f=x+y=10+10=20$$
$$x y=10(10)=100$$
No comments yet
Given $$\longrightarrow X Y=100 \quad x>0 \quad Y>0$$
$$f=x+y \quad$$ but $$\quad y=\frac{100}{x}$$
$$f=x+\frac{100}{x} \longrightarrow f^{\prime}(x)=1-\frac{100}{x^{2}} \rightarrow f^{\prime}(x)=\frac{x^{2}-100}{x^{2}}$$
$$f^{\prime}(x)=0 \longrightarrow \frac{x^{2}-100}{x^{2}}=0 \rightarrow x^{2}-100=0 \rightarrow(x+10)(x-10)=0$$
$$x=10, x=-10$$ rejected
$$x=10$$
Applying Second Derivative Test:
$$f^{\prime \prime}(x)=\frac{-100 (2 x)(-1)}{x^{4}}=\frac{200}{x^{3}}$$
$$f^{\prime \prime}(10)=\frac{200}{1000}>0$$
\ F has Iocal minimum at $$x=10$$
$$y=\frac{100}{x}=\frac{100}{10}=10$$
$$f=x+y=10+10=20$$
$$x y=10(10)=100$$
No comments yet
Join the conversation