2 years ago

A sailboat with a sick passenger abroad is following a parabolic path given by the equation = − 2 +2 + 8.

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

4 0

A sailboat with a sick passenger aboard is following a parabolic path given by the equation y=-2x+8. T...

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Read 2 more answers

For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?

sergey [27]

Answer:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

Step-by-step explanation:

Given

$f(x) = \frac{7}{2}x - 16$

Required

The difference quotient for h

The difference quotient is calculated as:

$\frac{f(x + h) - f(x)}{ h}$

Calculate f(x + h)

$f(x) = \frac{7}{2}x - 16$

$f(x+h) = \frac{7}{2}(x+h) - 16$

$f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16$

The numerator of $\frac{f(x + h) - f(x)}{ h}$ is:

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)$

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16$

Collect like terms

$f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16$

$f(x + h) - f(x) = \frac{7}{2}h$

So, we have:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h$

Rewrite as:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}$

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

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