Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

4x-x^(2)y+y^(3)=10
Find the value of
(dy)/(dx) at the point
(1,2).
Choose 1 answer:
(A) 0
(B)
(2)/(3)
(C) -1
(D) -4

$4 x-x^{2} y+y^{3}=10$ $\newline$ Find the value of $\frac{d y}{d x}$ at the point $(1,2)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $\frac{2}{3}$ $\newline$ (C) $-1$ $\newline$ (D) $-4$

View step-by-step help

View step-by-step help

Transformations of quadratic functions

Full solution

Q.

4 x-x^{2} y+y^{3}=10

\newline

Find the value of

\frac{d y}{d x}

at the point

(1,2)

.

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

\frac{2}{3}

\newline

(C)

-1

\newline

(D)

-4

Apply Rules and Derivatives: Now, apply the product rule to the term $-x^2y$ and the chain rule to $y^3$ . $\newline$ $\frac{d}{dx}(4x) - \frac{d}{dx}(x^2y) + \frac{d}{dx}(y^3) = 0$ $\newline$ $4 - (2xy + x^2\frac{dy}{dx}) + 3y^2\frac{dy}{dx} = 0$
Substitute Point into Equation: Substitute the point $(1,2)$ into the differentiated equation. $\newline$ $4 - (2\cdot 1\cdot 2 + 1^2\frac{dy}{dx}) + 3\cdot 2^2\frac{dy}{dx} = 0$ $\newline$ $4 - (4 + \frac{dy}{dx}) + 12\frac{dy}{dx} = 0$
Simplify and Solve for $\frac{dy}{dx}$ : Simplify the equation and solve for $\frac{dy}{dx}$ . $4 - 4 - \frac{dy}{dx} + 12\frac{dy}{dx} = 0$ $0 = \frac{dy}{dx}(12 - 1)$ $\frac{dy}{dx} = \frac{0}{11}$ $\frac{dy}{dx} = 0$

More problems from Transformations of quadratic functions

Question

h

is defined over the real numbers. This table gives a few values of

h

\newline

\begin{tabular}{lllll}

\newline

x

-6

1

-6

01

-6

001

-5

9

\newline

h(x)

-0

25

-0

74

-0

98

-1

0

\newline

\newline

What is a reasonable estimate for

\lim _{x \rightarrow-6} h(x)

\newline

1

\newline

-6

\newline

-2

\newline

-1

\newline

(D) The limit doesn't exist

Posted 4 months ago

Question

What is the amplitude of

\newline

g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ?

\newline

Posted 4 months ago

Question

What is the amplitude of

y=5 \sin (4 x-2)-3

\newline

Posted 4 months ago

Question

What is the amplitude of

y=-3 \cos (\pi x+2)-6 ?

\newline

Posted 4 months ago

Question

What is the amplitude of

y=3 \sin (2 x-1)+4

\newline

Posted 4 months ago

Question

What is the period of the function

h(x)=-3 \cos (\pi x+2)-6 ?

\newline

Give an exact value.

\newline

Posted 4 months ago

Question

What is the period of the function

\newline

h(x)=5 \sin (4 x-2)-3 \text { ? }

\newline

Give an exact value.

\newline

Posted 4 months ago

Question

What is the period of the function

g(x)=2 \cos (7 x+5)+1 ?

\newline

Give an exact value.

\newline

Posted 4 months ago

Question

What is the period of the function

f(x)=3 \sin (2 x-1)+4

\newline

Give an exact value.

\newline

Posted 4 months ago

Question

What is the period of the function

f(x)=-4 \cos (5 x-9)-7

\newline

Give an exact value.

\newline

Posted 4 months ago