Question
Asked Nov 28, 2019
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please answer both

Find the points on the curve where the tangent is horizontal or vertical.
1. 3t, y t2 -3
2. 2cos0, y= sin 20.
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Find the points on the curve where the tangent is horizontal or vertical. 1. 3t, y t2 -3 2. 2cos0, y= sin 20.

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Expert Answer

Step 1

Given:

(a). x -3t y = t2 -3
(b). x 2cos, y = sin 20
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(a). x -3t y = t2 -3 (b). x 2cos, y = sin 20

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Step 2

(a). Differentiate ‘x’ and ‘y’ with respect to ‘t’:

d
)-)()
(1)
dt
(x)
dt
3r2 -3
dt
dt
dx
음아올마음이
d
d
-(y)
dt
)=)()
(3)
dt
dt
dy
= 2
dt
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d )-)() (1) dt (x) dt 3r2 -3 dt dt dx 음아올마음이 d d -(y) dt )=)() (3) dt dt dy = 2 dt

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Step 3

Now, find dy/dx by [1] and [2] and find the...

2t
dx dx3t2 -3
dt
for horizontal tangents, we have slope
dy
2t
0
3t2-3
2t 0
t = 0
Put the value of 't in given equation
x =-3t= (0)'-3-0
y =-3= (0)-3 =-3
Therfore, at (0,-3), the tangent is horizontal.
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2t dx dx3t2 -3 dt for horizontal tangents, we have slope dy 2t 0 3t2-3 2t 0 t = 0 Put the value of 't in given equation x =-3t= (0)'-3-0 y =-3= (0)-3 =-3 Therfore, at (0,-3), the tangent is horizontal.

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Tagged in

Math

Calculus

Derivative