First slide

Rate Measure

Question

The slope of the tangent to the curve represented by $x = t^{2} + 3 t - 8 and y = 2 t^{2} - 2 t - 5$ at the point $M (2, - 1)$ is

Moderate

A

7/6
B

2/3
C

3/2
D

6/7

Solution

We first determine the value of t corresponding to the given values of $x and y .$
From $t^{2} + 3 t - 8 = 2, w e g e t t = 2, - 5,$ and from $2 t^{2} - 2 t - 5 = - 1, we get t = 2, - 1.$

Hence to the given point there corresponds the value $t = 2.$

Therefore , the slope of the tangent at $(2, - 1)$ is

$y^{'} |_{t = 2} = \frac{d y / d t}{d x / d t} |_{t = 2} = \frac{4 t - 2}{2 t + 3} |_{t = 2} = \frac{6}{7}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App