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alisha [4.7K]
1 year ago
15

To Enter the value of n that makes the equation: 4^5.4^n=4^8 true

Mathematics
1 answer:
irina1246 [14]1 year ago
6 0
4^2\text{ }\times4^n=4^8

Since both sides have the same base (4), we can add the exponents

4^{5+n}=4^85+n=8

subtract 5 from both sides:

5+n-5=8-5n=3

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4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).

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</span>

<span>⇒ (x + 2)³ = -1 ⇒ x + 2 =  1 ⇒ x = - 1
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8) y-intercepts ⇒ x = 0

y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
</span><span>
</span><span>
</span><span>ii) second derivative: to determine where x = - 2  is a local maximum, a local  minimum, or an inflection point.
</span><span>
</span><span>
</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x =  -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>


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