An equation for the tangent line to the curve $y = \left( x ^ { 2 } + x - 1 \right) ^ { 3 }$ at the point where x = 1 is:
A)y = 2x + 1
B)y = 9x - 1
C)y = 9x
D)y = 9x - 8

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, first find the derivative of $y = (x^2 + x - 1)^3$ using the chain rule. Then evaluate the derivative at $x = 1$ to find the slope of the tangent line. The point on the curve at $x = 1$ is $(1, 1)$. Using the point-slope form of a line, the equation of the tangent line is $y = 9x - 8$.

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

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