24. Estimate instantaneous rate of change of each function at the given x value using a centered interval of ±0.001. a) f(x)=x² +x² at x =2 b) f(x)=-x* +1 at x = 3

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A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: 6) Use derivatives to find where the function is concave up f(x)=x.e2x*

A: If  f "(x) > 0  on an interval, then f(x) is concave up on that interval.

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A: px=4-3xx4+7x3

Q: f" (x) 0, nn +4 f' (n) = −n f' (n + 4) = n +1 f(n) = n f(n+4)=n+7

A: The given condtions are

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A: The given function is  f(x) = x3 + x Differentiate with respect to x , we get f'(x) = 3x2 + 1

Q: 8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0

A: Step 1:   Step 2: Step 3: Step 4:

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A:

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A: Given function, g(x) = 12 - 5x  a) The formula for average rate of change of a function g(x) on…

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A:

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A:

Q: Evaluate f'(a) for the function f(x)= 2x² – 5x+1 What does f'(a) represent?

A: NOTE: Refresh your page if you can't see any equations. . take derivative take x=a

Exponential Growth Model

The relation that represents an exponential function is: