Question
The minimum value of $x y$ is, if $a^{2} x^{4}+b^{2} y^{4}=c^{6}$(a) $\frac{c^{3}}{\sqrt{a b}}$(b) $\frac{c^{3}}{\sqrt{2 a b}}$(c) $\frac{c^{3}}{a b}$(d) $\frac{c^{3}}{2 a b}$
Step 1
Step 1: We are given the equation $a^{2} x^{4}+b^{2} y^{4}=c^{6}$ and we need to find the minimum value of $xy$. Show more…
Show all steps
Your feedback will help us improve your experience
Ankit Singh and 60 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $x, y, a, b, c$ are $>0$, the maximum value of $x y$ when $a^{2} x^{4}+b^{2} y^{4}=c^{6}$ is (a) $\frac{c^{3}}{2 a b}$ (b) $\sqrt{\frac{c^{3}}{2 a b}}$ (c) $\frac{c^{3}}{\sqrt{2 a b}}$ (d) $\frac{c}{2 \sqrt{a b}}$
The min. value of $a x+b y$ when $x y=r^{2}$ is (a) $2 r \sqrt{a b}$ (c) $2 a b \sqrt{r}$ (c) $-2 r \sqrt{a b}$ (d) None
The Maxima and Minima
Level II
Absolute Minimum If $a, b,$ and $c$ are positive constants, show that the minimum value of $f(x)=a e^{c x}+b e^{-c x}$ is $2 \sqrt{a b}$.
Applications of the Derivative
Optimization
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD