Find an equation for the tangent line to the curve $y = \left( 7 x ^ { 2 } + x - 1 \right) ^ { 3 }$ at the point where x = 0.
A) y = 14x + 1
B) y = 24x + 3
C) y = 3x + 1
D) y = 3x - 1

Question

Quizplus · Accepted Answer

To find the tangent line, first find the derivative of $y$ and evaluate it at $x = 0$. The derivative is $y' = 3(7x^2 + x - 1)^2 \cdot (14x + 1)$. At $x = 0$, $y' = 3(-1)^2 \cdot 1 = 3$. The point on the curve at $x = 0$ is $(0, -1)$. The equation of the tangent line is $y = 3x - 1$.

Find an Equation for the Tangent Line to the Curve y=(7x2+x−1)3y = \left( 7 x ^ { 2 } + x - 1 \right) ^ { 3 }y=(7x2+x−1)3

Find an Equation for the Tangent Line to the Curve $y = \left( 7 x ^ { 2 } + x - 1 \right) ^ { 3 }$