Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y= $2 x^{2}$ and the slope of tangent is tan $θ = \frac{d y}{d x} = 4 x$ .

$\begin{matrix} x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200 \end{matrix}$

Open in App

Solution

The graph y = $2 x^{2}$ should be drawn by the students on a graph paper for results. To find slope at any point, draw a tangent at the point and extend the line to meet x-axis. Then, find tan $θ$ as shown in the figure.

Suggest Corrections

Similar questions

Q. Draw a graph from the following data. Draw tangents at x = 2, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x² and the slope of tangent is

\tan θ = \frac{d y}{d x} = 4 x

\begin{matrix} x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200 \end{matrix}

Normals are drawn from a point P(h, k) with slopes $m_{1}, m_{2}, m_{3}$ to the parabola $C_{1} : y^{2} = 4 x$

If the curve C is the locus of point P with $m_{1} m_{2} = 2$ , then number of common tangents to the curve $C_{1}$ and curve C is

Question 7

In which of the following cases, do the quantities vary directly with each other?
$(a) \begin{matrix} x & 0.5 & 2 & 8 & 32 y & 2 & 8 & 32 & 128 \end{matrix}$
$(b) \begin{matrix} p & 1^{2} & 2^{2} & 3^{2} & 4^{2} q & 1^{3} & 2^{3} & 3^{3} & 4^{3} \end{matrix}$
$(c) \begin{matrix} r & 2 & 5 & 10 & 25 & 50 s & 25 & 10 & 5 & 2 & 0.5 \end{matrix}$
$(d) \begin{matrix} u & 2 & 4 & 6 & 9 & 12 v & 18 & 9 & 6 & 4 & 3 \end{matrix}$

Q. Find the slope of the tangent to the curve

y = 4 x^{2} - 3 x - 8

at point

(- 3, 4)

Q. The sum of the slopes of the tangents to the parabola

y^{2} = 8 x

drawn from the point (–2, 3) is

Join BYJU'S Learning Program

Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y=2x2 and the slope of tangent is tan θ=dydx=4x. x12345678910y281832507298128162200

The graph y =2x2 should be drawn by the students on a graph paper for results. To find slope at any point, draw a tangent at the point and extend the line to meet x-axis. Then, find tan θ as shown in the figure.

The graph y = $2 x^{2}$ should be drawn by the students on a graph paper for results. To find slope at any point, draw a tangent at the point and extend the line to meet x-axis. Then, find tan $θ$ as shown in the figure.