Write the equation of the line tangent to f(x)=\tan x+3

Talamancoeb

Talamancoeb

Answered question

2021-12-16

Write the equation of the line tangent to f(x)=tanx+3 at (π4,4)
Find all values of x such that the tangent line to f(x)=(x29)2 is horizontal.

Answer & Explanation

Stella Calderon

Stella Calderon

Beginner2021-12-17Added 35 answers

Given f(x)=tanx+3
y=f(x)=tanx+3
derivative f(x) with repect to 'x'
ddxf(x)=ddx(tanx+3)
f(x)=sec2x+0
dydx=sec2x
Slope m=dydzx=π4=sec2π4
=sec2(π4)
=(2)2
=2
Equation of tangent line is (yy1)=m(xx1)
where (x1,y1)=(π4,4) and m=2
(y4)=2(xπ4)
y=2xπ2+4
y=2xπ+82
zesponderyd

zesponderyd

Beginner2021-12-18Added 41 answers

Given f(x)=(x2a)2
y=f(x)
Slope horizontal means dydx=0
dydx=ddx(x2a)2
=2(x2a)ddx(x2a)
=2(x2a)(2x)
=4x(x2a)
dydx=04x(x2a)=0
x29=0
x2=9
x=±3
x value are 3,3,0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?