What-is-the-area-of-the-region-bounded-by-coordinate-axis-and-the-line-tangent-to-the-graph-y-1-8-x-2-1-2-x-1-at-the-point-0-1-

Question Number 18642 by tawa tawa last updated on 26/Jul/17

What is the area of the region bounded by coordinate axis and the line

tangent to the graph, y = \frac{1}{8} x^{2} + \frac{1}{2} x + 1, at the point (0, 1)

Answered by Tinkutara last updated on 26/Jul/17

\frac{d y}{d x} = \frac{x}{4} + \frac{1}{2}

Slope of the tangent at x = 0 is \frac{1}{2} .

∴ Equation of tangent is

y - 1 = \frac{x}{2} \Rightarrow y = \frac{x}{2} + 1

Intercepts of this line are (0, 1) and

(- 2, 0) .

∴ Area of this triangle = \frac{1}{2} \times 2 \times 1

= 1 sq . unit

Commented by tawa tawa last updated on 26/Jul/17

God bless you sir