Help ! The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative.
@hartnn

Question

Help ! The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative. 
@hartnn

anonymous · Answer

Differentiate s(t) with respect to time$$s'(t) = -9$$So the velocity is now independent of time meaning that velocity is always -9 no matter what.
The instantaneous velocity at t=1 is -9

twalt13 · Answer

thats  it ? what about the -8

phi · Answer

the derivative of s(t) is done term by term.   the derivative of a constant is 0

anonymous · Answer

The -8 relates to the position of the object and so when differentiated the -8 is irrelevant

twalt13 · Answer

thanks

twalt13 · Answer

i need you guys help on 1 more question though

anonymous · Answer

Shoot

twalt13 · Answer

Find the derivative of f(x) = -12x2 + 9x at x = 6.  i tried to work this out but always got stuck

anonymous · Answer

Ok when finding the derivative of something. Let's imagine we have something like$$ax^b$$Where a and b are just random numbers. When we differentiate it it will become$$a \times bx^b-^1$$So what we do is take the power down and take one off it!

For example $$5x^3 => 10x^2$$Does that make sense so far?

twalt13 · Answer

yea

anonymous · Answer

Sorry the $$-12x^2 => -24x$$

anonymous · Answer

If the power of the x is only 1 (as in your case with 9x) we still do the same thing$$9x^1=>9x^0$$However x^0 is the same as 1 Therefore it is the same as writing$$9x=>9$$

anonymous · Answer

Any questions on that?

twalt13 · Answer

nope im following you

anonymous · Answer

Great, so far we know what each term differentiates to, so all we need to do is substitute in x=6 into what we were left with. Our equation so far is$$f'(x) = -24x +9$$Subbing in our value for x I reckon I can leave to you?

twalt13 · Answer

yes thanks man