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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    Please show your work so I can see what you did. Thanks.

  2. Xishem
    • 4 years ago
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    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

  3. anonymous
    • 4 years ago
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    could you explain the differentiating part for me please

  4. anonymous
    • 4 years ago
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    i understand it somewhat but would appreciate a clear explanation

  5. anonymous
    • 4 years ago
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    ?

  6. Xishem
    • 4 years ago
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    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?

  7. anonymous
    • 4 years ago
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    yes, THANKS!!!

  8. Xishem
    • 4 years ago
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    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.

  9. anonymous
    • 4 years ago
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    ok

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