Slope of a line bounded by a parabola

Question

a line runs through the origin that divides the region bounded by the parabola y = 2 x - 6 x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Answer 1

From the given data have to find out the slope of the tangent line to the curve y = 2x - 6x ^2.

Let m be the slope of the tangent line to the curve y = 2x - 6x ^2 at the origin (0, 0).

We can use implicit differentiation to find y '.

Slope (m ) = y ' = 2 - 12x.

Substitute the value x = 0.

m = 2 - 12( 0 )

    = 2 - 0

    = 2.

This is the slope (m ) of the tangent line to the implicit curve at (0, 0).

Therefore, slope of the line is 2.

Observe the graph :