Answered

Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P: y = 9x^2 + 5 ; P (2,41)

Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P: y = 9x^2 + 5 ; P (2,41) class=

Answer :

jjthomson93

Answer:

(a) 36

(b) y = 36x-31

Step-by-step explanation:

(a) dy/dx = 18x

slope of tangent at (2, 41) = 18(2)

= 36

(b) using y-y1 = m(x-x1)

y-41 = 36(x-2)

y = 36x-31

okpalawalter8

W have that the slope of the curve at the given point P and tangent line at P are

[tex]m=36[/tex]

[tex]y=36x-72+41[/tex]

From the Question we have that

[tex]y = 9x^2 + 5\\\\P(2,41)[/tex]

a)

We start by differentiating the equation

[tex]y = 9x^2 + 5[/tex]

[tex]\frac{dy}{dx}=18x[/tex]

[tex]y'=18x[/tex]

Therefore

[tex]At x=2[/tex]

[tex]m=18(2)[/tex]

[tex]m=36[/tex]

b)

Generally the equation for Tangent line at P(2,41)  is mathematically given as

With slope at 36

[tex]y-(41)=36(x-2)[/tex]

[tex]y=36x-72+41[/tex]

In conclusion

The  slope of the curve at the given point P and tangent line at P are

[tex]m=36[/tex]

[tex]y=36x-72+41[/tex]

For more information on this visit

https://brainly.com/question/3605446

Other Questions