How do you find the equation of the tangent line to the curve y=4x−1 at point of (0,-4)?

Differentiate using the quotient rule to find the instantaneous rate of change of the function at x=0.y′=0(x−1)−4(1)(x−1)2y′=−4(x−1)2The instantaneous rate of change at x=a is given by f'(a).mtangent=−4(0−1)2mtangent=−41mtangent=−4The equation can now be obtained.y−y1=m(x−x1)y-(-4)=-4(x-0)y+4=-4xy=-4x-4

"How do you find the equation of the..." was answered by our experts

High School
Calculus and Analysis
Calculus 1
Derivatives

Jefferson Pacheco

Answered question

2022-04-15

How do you find the equation of the tangent line to the curve

y = \frac{4}{x - 1}

at point of (0,-4)?

Answer & Explanation

legaldaj1dn

Beginner2022-04-16Added 9 answers

Differentiate using the quotient rule to find the instantaneous rate of change of the function at x=0.
$y^{'} = \frac{0 (x - 1) - 4 (1)}{{(x - 1)}^{2}}$
$y^{'} = - \frac{4}{{(x - 1)}^{2}}$
The instantaneous rate of change at x=a is given by f'(a).
$m_{tangent} = - \frac{4}{{(0 - 1)}^{2}}$
$m_{tangent} = - \frac{4}{1}$
$m_{tangent} = - 4$
The equation can now be obtained.
$y - y_{1} = m (x - x_{1})$
y-(-4)=-4(x-0)
y+4=-4x
y=-4x-4

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