Unit Test
2 answers:
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The function is 
, and according to the description of the function in the problem statement, we have the following:
at t=0 after being thrown (that is, at initial time), the height of the ball is calculated by h(0) as follows:
(ft), which is the initial height, as expected.
At t=1 (sec), the height would be
.
etc.
The path is parabolic, as we know by seeing that the function is a quadratic polynomial function. This function has been given in factored form as well. From that we can see that the zeros of the function are t=7 and t=-2.
This means that at t=7 sec, the height h is 0, which means that the ball has hit the ground. t=-2 has no significance in the context of our problem so we just neglect it.
Answer: B) 7 sec
at t=0 after being thrown (that is, at initial time), the height of the ball is calculated by h(0) as follows:
At t=1 (sec), the height would be
etc.
The path is parabolic, as we know by seeing that the function is a quadratic polynomial function. This function has been given in factored form as well. From that we can see that the zeros of the function are t=7 and t=-2.
This means that at t=7 sec, the height h is 0, which means that the ball has hit the ground. t=-2 has no significance in the context of our problem so we just neglect it.
Answer: B) 7 sec
Answer:
Step-by-step explanation:
In single-variable calculus, the difference quotient is the expression
,
which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).
This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.
.
Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as <em>h</em> approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.
Therefore,
