a.
b.
The metal obey this law for values of strain until 0.05, where we have a linear relationship (each increase of 0.01 in the strain causes an increase of 100 in the stress). After this point, we don't have a linear relationship anymore.
c. Since an increase of 0.01 in the strain causes an increase of 100 in the stress, the slope is:

Now, calculating the coefficient b (y-intercept), we have:

So the equation is:

d.
The maximum value of stress is 560, and occurs at strain = 0.07.
Answer:
y intercept (0, 4)
x intercept (4, 0)
I hope this is good enough:
<h3>
Answer: Choice A</h3>
Explanation:
Each table has x = 10 in it. Plug this value into the given equation.
y = -2x+17
y = -2*10+17
y = -20+17
y = -3
The input x = 10 leads to the output y = -3. Table A shows this in the middle-most row. So that's why choice A is the answer. The other tables have x = 10 lead to y values that aren't -3 (eg: choice D has x = 10 lead to y = 12), so we can rule them out.
By definition of absolute value, you have

or more simply,

On their own, each piece is differentiable over their respective domains, except at the point where they split off.
For <em>x</em> > -1, we have
(<em>x</em> + 1)<em>'</em> = 1
while for <em>x</em> < -1,
(-<em>x</em> - 1)<em>'</em> = -1
More concisely,

Note the strict inequalities in the definition of <em>f '(x)</em>.
In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:


All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.
It would be at 35 when you work all then problems together