Final answer:
To find the point on the curve y=4x+3 closest to the point (0,7), we can calculate the perpendicular distance from (0,7) to the curve and find the point with the smallest distance.
Step-by-step explanation:
To find the point on the curve y=4x+3 closest to the point (0,7), we need to find the point on the curve that has the smallest distance to (0,7). This can be done by finding the perpendicular distance from (0,7) to the curve y=4x+3.
The perpendicular distance from a point (x1,y1) to a line y=mx+c is given by the formula:
d = |y1 - mx1 - c| / sqrt(m^2 + 1)
Plugging in the values for the equation y=4x+3, we can calculate the distance d and find the point on the curve closest to (0,7).