Find an equation of the line tangent to the graph of $y = 7 ^ { x } + 2$ at the point $( 0,3 )$.
A) $y = ( \ln 7 ) x + 3$
B) $y = 7 x + 3$
C) $y = 7 x + 2$
D) $y = ( \ln 7 ) x + 2$

Question

Quizplus · Accepted Answer

The derivative of $y = 7^x + 2$ with respect to $x$ gives the slope of the tangent line at any point $x$, which is $y' = 7^x \ln 7$. At $x = 0$, $y' = 7^0 \ln 7 = \ln 7$. Thus, the equation of the tangent line at $(0,3)$ is $y = (\ln 7)x + 3$.

Find an Equation of the Line Tangent to the Graph y=7x+2y = 7 ^ { x } + 2y=7x+2

Find an Equation of the Line Tangent to the Graph $y = 7 ^ { x } + 2$