Question

Let -pi/4 < x < pi/4 , f(x)=tan(2x). A tangent to the graph of y=f(x) where x= a makes an angle of 70 degrees with the positive direction of the x-axis. Find the possible values of a

Answer 1

x=a=70 degrees = 7pi/18

Answer 2

what should i do next?

Answer 3

@tkhunny

Answer 4

@ganeshie8 help please

Answer 5

Have you considered the 1st Derivative?

\(\tan(70º) = 2.7475\)

Answer 6

no

Answer 7

Why not? Is this for a calculus class?

Answer 8

so do we take the derivative of f(x)?

Answer 9

yes

Answer 10

If you want to know the slope of a tangent line, ALWAYS think about the 1st Derivative. Write it on your forehead if you have to.

Answer 11

but they are asking me to find the possible values of a

Answer 12

i get u

Answer 13

7pi/18 is not within the interval

Answer 14

Who said it was? Read the problem statement again until you understand what it wants.

Answer 15

yes your right because they mentioned the tangent to the graph

Answer 16

Did you find the derivative? Start there.

Answer 17

f'(x)=2sec^2(2x)

Answer 18

Perfect. Now, is there a spot or two in \([-\pi/4,\pi/4]\) where f'(x) takes on tan(70º)?

Answer 19

between 45 degrees and 315 degrees?

Answer 20

No, between -45º and +45º. Not the same thing.

Answer 21

then how could -45degrees be expressed as a positive angle

Answer 22

I think you are confusing 70º with something on the x-axis that you seek. It's just a number, tan(70º) = 2.747 or so. Find a value of x, between -pi/4 and pi/4, where f'(x) = 2.747 or so. 70º has little to do with anything. It's just a target number for the derivative.

Answer 23

Your challenge is to find the location of the green and light-blue lines.