Find the equation of the tangent line to the graph of f at the given point.
-$f ( x ) = x ^ { 2 } + 5 x$ at $( 4,20 )$
A) $y = 2 x + 5$
B) $y = 2 x - 5$
C) $y = 13 x - 32$
D) $y = 13 x - 72$

Question

Quizplus · Accepted Answer

To find the equation of the tangent line to the graph of $f(x) = x^2 + 5x$ at the point $(4,20)$, we first need to find the derivative of $f(x)$, which gives us the slope of the tangent line at any point $x$. The derivative $f'(x) = 2x + 5$. Evaluating this derivative at $x = 4$ gives $f'(4) = 2(4) + 5 = 13$, which is the slope of the tangent line at the point $(4,20)$. To find the equation of the tangent line, we use the point-slope form of a line: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through. Substituting $m = 13$, $x_1 = 4$, and $y_1 = 20$ gives $y - 20 = 13(x - 4)$. Simplifying this equation gives $y = 13x - 52 + 20$, which simplifies further to $y = 13x - 32$.

Find the Equation of the Tangent Line to the Graph f(x)=x2+5xf ( x ) = x ^ { 2 } + 5 xf(x)=x2+5x

Find the Equation of the Tangent Line to the Graph $f ( x ) = x ^ { 2 } + 5 x$