Question

question use implicit differentiation to find the equation of the tangent line to the function defined implicitly by the equation below at the point (-2, -1). 4x^2 - y^2 = 15 give your answer in the form y = mx + b. provide your answer below:

Explanation:

Step1: Differentiate implicitly

Differentiate $4x^{2}-y^{2}=15$ with respect to $x$: $8x - 2y\frac{dy}{dx}=0$.

Step2: Solve for $\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{4x}{y}$.

Step3: Find slope at point

Substitute $x = - 2$ and $y=-1$ into $\frac{dy}{dx}$: $m=\frac{4\times(-2)}{-1}=8$.

Step4: Find $b$

Use $y=mx + b$ with $x=-2,y = - 1,m = 8$: $-1=8\times(-2)+b$, so $b = 15$.

Answer:

$y = 8x+15$