Find the equation of the tangent line to the graph of $f ( x ) = x ^ { 2 } + 1$ at the point (4, 17).
A) y = 8x - 15
B) Not defined
C) y = 17
D) x = 4

Question

Quizplus · Accepted Answer

The slope of the tangent line to the curve at any point is given by the derivative of the function at that point. For $f(x) = x^2 + 1$, the derivative $f'(x) = 2x$. At $x = 4$, the slope is $f'(4) = 2(4) = 8$. The equation of the tangent line can be found using the point-slope form: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point of tangency. Substituting $m = 8$ and $(x_1, y_1) = (4, 17)$, we get $y - 17 = 8(x - 4)$, which simplifies to $y = 8x - 15$.

Find the Equation of the Tangent Line to the Graph f(x)=x2+1f ( x ) = x ^ { 2 } + 1f(x)=x2+1

Find the Equation of the Tangent Line to the Graph $f ( x ) = x ^ { 2 } + 1$