When is the instantaneous rate of change of f (x) = 4(2)^(3x)+ 7 equal to 1000? Round your answer to 2 decimal places, if necessary.
Added by Nicholas M.
Step 1
Using the chain rule and the properties of derivatives, we have: \[ f'(x) = \frac{d}{dx} [4(2)^{3x} + 7] \] \[ f'(x) = 4 \cdot \frac{d}{dx} [(2)^{3x}] \] \[ f'(x) = 4 \cdot (2)^{3x} \cdot \ln(2) \cdot \frac{d}{dx} [3x] \] \[ f'(x) = 4 \cdot (2)^{3x} \cdot \ln(2) Show more…
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