Question

Evaluate the derivative at the given value of x.
y = 4 - 2x2; x = 1

Answer 1

simply find dy/dx and put x=1 answer is -4 if u have x^2

Answer 2

For some reason I came up with 0

Answer 3

i am going to make a guess, that you have not gotten to "techniques of differentiation" yet, aka power rule, chain rule, etc and you have to do this by hand i.e. by computing a limit

Answer 4

sorry that was x^2

Answer 5

correct

Answer 6

so you have
\[f(x)=4-2x^2\] and it is your job to compute
\[\lim_{x\to 1}\frac{f(x)-f(1)}{x-1}\] am i right?

Answer 7

yes

Answer 8

ok this is going to require first knowing that \(f(1)=4-2=2\)

Answer 9

dy/dx wil be -4x here x=1 so answr is -4

Answer 10

then doing some algebra

Answer 11

forget about the limit for a minute, lets just compute
\[\frac{f(x)-f(2)}{x-1}=\frac{4-2x^2-2}{x-1}\] the algebra is pretty easy for this one

Answer 12

combining like terms in the numerator gives
\[\frac{2-2x^2}{x-1}\] factor out the \(2\) get \[\frac{2(1-x^2)}{x-1}\] then factor the difference of two square
\[\frac{2(1-x)(1+x)}{x-1}\] and finally note that \(\frac{1-x}{x-1}=-1\) making the whole thing
\[-2(1+x)\]

Answer 13

your job is to compute the limit, which means you would like to replace \(x\) by \(1\) but you cannot while you have an \(x-1\) in the denominator, so all the work was to factor and cancel so you do not have an \(x-1\) in the denominator

Answer 14

I have been taking these notes down for the next. So I needed to factor out the x-1 so I could compute the limit

Answer 15

now that the denominator is gone , you are free to replace \(x\) by \(1\) and get
\[-2(1+1)=-4\]as your answer

Answer 16

yes, your job is always (if possible) factor and cancel so you no longer have a zero in the denominator

Answer 17

Got it. thanks again. As you can tell I have been having some trouble with calculus