Question:
There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.
My work is attached.
Any help would be greatly appreciated!
Thanks in advance!
Question:
There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.
My work is attached.
Any help would be greatly appreciated!
Thanks in advance!
A tangent line passing through $\displaystyle (6,35)$ may not have a slope of value $\displaystyle 2\cdot 6=12$ there, as the slope of such a line is constant even when $\displaystyle x$ varies. What we're really looking for are values of $\displaystyle x_0$ such that
$\displaystyle y-y_0=2x_0(x-x_0)$
passes through $\displaystyle (6,35)$.
There are two tangent lines ...Your worksheet shows an equation for a line (1 line).which pass through the point (6,35).
Find the x-coordinates of the points of tangency.!
You need to show the x coordinate of the line that is tangent to the curve $\displaystyle y=x^2$ AND passes thorough (6,35) [for this line x<6].
& the x coordinate of the line that is tangent to the curve $\displaystyle y=x^2$ AND passes thorough (6,35) [for this ine x>6].
The two tangent lines will intersect at (6,35).
You will have two lines:
LINE 1:
$\displaystyle y_1 = 2x_1 + b$ (that passes thorough (6,35) AND is tangent to $\displaystyle y=x^2$
LINE 2:
$\displaystyle y_2 = 2x_2 + c$ (that passes thorough (6,35) AND is tangent to $\displaystyle y=x^2$
You are looking for x1 and x2.
See the posts by Scott H (& hjortur) it is almost solved.