Find the value of c in the figure above, where the line l tangent to the graph of y = 5x at (0, 1) intersects the x -axis. Enter the exact answer. Solution dy/dx = 5^x*ln(5) dy/dx at x=0 is ln(5) Equation of tangent is y-1 = xln(5) y = 1 + x*ln(5) 0 = 1 + c*ln(5) c = -1/ln(5) = -0.621.

1. Find the value of c in the figure above, where the line l tangent to the graph of y = 5x at (0, 1)
intersects the x -axis. Enter the exact answer.
Solution
dy/dx = 5^x*ln(5)
dy/dx at x=0 is ln(5)
Equation of tangent is y-1 = xln(5)
y = 1 + x*ln(5)
0 = 1 + c*ln(5)
c = -1/ln(5) = -0.621