find,if any, an equation for a common tangent line to these 2 curves:5x^2;and 5x^2-x+6
To find the equation for the common tangent line to the curves 5x^2 and 5x^2 - x + 6, we need to find the point(s) of tangency and the slope of the tangent line at that point.
Step 1: Find the derivative of both curves.
The derivative of 5x^2 is 10x, and the derivative of 5x^2 - x + 6 is 10x - 1.
Step 2: Set the derivatives equal to each other.
10x = 10x - 1
Step 3: Solve for x.
10x - 10x = -1
0 = -1
Since the equation 0 = -1 has no solution, there are no points of tangency between the two curves. This means there is no common tangent line for 5x^2 and 5x^2 - x + 6.
Therefore, the common tangent line does not exist for these two curves.