Answer:
5.463 hours
Step-by-step explanation:
Given you are driving north from home such that your distance is f(x) = -4x³ +25x² +85x +51 miles at time x, you want to know the time you are farthest north of home.
Local maximum
The local maximum in the distance function will be located where the derivative is zero.
f'(x) = -12x² +50x +85
The zero of this can be found using the quadratic formula with a=-12, b=50, c=85:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-50\pm\sqrt{50^2-4(-12)(85)}}{2(-12)}\\\\\\x=\dfrac{50\pm\sqrt{6580}}{24}=\{-1.297,5.463\}[/tex]
You will be farthest from home after 5.463 hours.
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