The best way that we can find the
answer to this question is to set the equation equal to y. Once we have done that we can then find what
the derivative of -5x-5 is.
The derivative of the equation -5x-5 is
just the equation of the slope at every single point along the line of
-5x-5. Since this equation is actually
just a line, we should find the value of the derivative to be a constant
number. Now we just setup the equation
to take it’s derivative below.
·
What is -5x-5 when we take the derivative?
Now when we take a derivate, we take the
form of the variable and subtract its exponent by 1. Once we do that we then multiply the variable
by the previous value of the exponent as shown above. We now get the actual answer for the
derivative below. As we know that when the value of an exponent of 0 makes the
coefficient 1.
As we can now see, we get the derivative
to be -5, which makes sense because the slope of a line is constant (it never
changes) which means that the value of the derivative will also be
constant. Now let’s find the integral of
this equation;
·
What is -5x-5 when we take the integral?
The first step that we need to take is
separarate both of the coefficients in order to find both of their integrals.
The next step we need to take is to set
the constant of both integrals outside of both integrals.
Now that we have the equation in the form
of a proper integral, we can now find it. In order to take the integral, we
need to add 1 to the exponent of the variable and divide it by the new value
for the exponent.
Now we find the integral to be the
equation above. The integral shows the
area under the line of -5x-5 where C is a constant based on what the initial
position of the graph could be. This
shows that the area underneath the line changes for every value of x along the
line. What we have as the integral is a
quadratic formula that decreases more and more rapidly the larger the value of
x becomes.
For a similar problem check out How Do We Solve -6x-6 When Set Equal to Zero?
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