Slope of a function problem

blahblahbla

Hey guys Im trying to teach myself calculus and found some good online rescores at
http://www.youtube.com/user/khanacademy
but when I tried to test one of the functions

sin(3x^5+2x)

I plugged this function into an online graph calculator at
http://www.coolmath.com/graphit/
in order to find the slope I have to get 1st derivative which is

(15x^4+2)cos(3x^5+2x)

So basically I just wanted to test the slope at different points so I looked at my graph and saw 0.7 would be a -slope since the function is decreasing at that point but my slope turns out to be 5.5, which is a positive.

(15(.7)^4+2)cos(3(.7)^5+2(.7))

(15(.240)+2) cos(3(0.168)+1.4

( 5.6)(cos(1.90))
5.6*0.999

slope= 5.5

What have I done wrong?
Should it be a -slope. its been years since Ive done the leaving cert my solve for x might be incorrect

bnt

Is your calculator set to Degrees? It needs to be Radians for this to work. You have the differential correct, but I get f(0.7) = 0.945, and f'(0.7) = -1.833.

PS: Yep - just tried it with calculator set to Degrees, I got 5.598. No biggie. :cool:

blahblahbla

bnt wrote: »

Is your calculator set to Degrees? It needs to be Radians for this to work. You have the differential correct, but I get f(0.7) = 0.945, and f'(0.7) = -1.833.

Yes it was set to degrees, How do you know when its time to change you calculator to Degrees Radian or Grads.
Whats the difference, when you multiply 2 numbers should we not always get the same answer or does it only apply to doubles or floats?

Thanks for the help!

bnt

But it's not simple multiplication, since the Trig functions are non-linear and periodic, based on the geometry of a vector inscribed inside a circle, and so the absolute magnitudes of the numbers do matter. 10*sin(0.5) is not the same as sin(5), whether you use degrees or radians.)

There's more than one reason why calculus specifically requires radians, which have to do with how the trig functions are defined - for example, the Taylor series' and their derivatives - and see here for a quick explanation of the importance of radians in trig. You can check this with a simple example: plot f(x)=sin(x) and f'(x)=cos(x), but if you don't use radians, the plots won't make sense, just as you found.

How do I know when to use degrees? If the question gives me degrees, or I'm asked for them - otherwise it's radians all the way. They become really important in mechanics too e.g. anything to do with forces due to rotation.