Suppose h(t) = t^2+14t+7. Find the instantaneous rate of change h(t) with respect to t at t=2.

Question

anonymous · Answer

Please show your work so I can see what you did. Thanks.

xishem · Answer

First differentiate with respect to t. This finds an equation for the rate of change:
h'(t) = 2t + 14

Then, simply substitute 2 into the equation to get:
h'(2) = 2(2) + 14 = 18

anonymous · Answer

could you explain the differentiating part for me please

anonymous · Answer

i understand it somewhat but would appreciate a clear explanation

anonymous · Answer

?

xishem · Answer

When you take the derivative of a function, you follow a set of rules.

The most basic rule you need to know is when you have just a constant in front of a variable to some power n. The general form for this type of differentiation is:

$$f(x) = x^n$$$$f'(x) = nx^{n-1}$$
In the case of this question, you can differentiate each term separately:
$$f(x)=t^2+14t+7$$$$f'(x)=2t^1+14t^0+0 = 2t+14$$

Whenever a constant is differentiated, it becomes 0. Does that make more sense now?

anonymous · Answer

yes, THANKS!!!

xishem · Answer

Keep in mind that the power rule only works when you have a constant in front of the variable you differentiating in respect to. If you have products or quotients of expressions, it doesn't work correctly.

anonymous · Answer

ok