The derivative of f(x) at x=3 is 2x=6 approaching from the left side (apply power rule to y=x^2). The derivative of f(x) at x=3 is m approaching from the right side. In order for the function to be differentiable, the limit of derivative at x=3 must be the same approaching from both sides, so m=6. Then, x^2=mx+b at x=3, plug in m=6, 9=18+b, so b=-9.
Answer:
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The first thing we have to do is to calculate the
midpoint of the min and max speeds. We are given that the min and max is 74 and
95 respectively. The midpoint is then calculated as (max+min) / 2. Therefore:
midpoint = (74 + 95) / 2 = 84.5
Next, we calculate the distance from the midpoint to the
endpoint by doing subtraction. Therefore:
min endpoint: 84.5 – 74 = 10.5
max endpoint: 95 – 84.5 = 10.5
Now we know that v minus the midpoint will equal the
distance such that:
| v - midpoint | = distance.
To our problem,
| v – 84.5 | = 10.5
Answer: Option B- The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60
