help !!! Given the facts that f(9) = 11 and f'(9) = 3, use the difference quotient to estimate the value of f( 9.5 ). f(9.5) ~=

Question

anonymous · Answer

$$f^2=2f*f'$$

anonymous · Answer

what is that?

anonymous · Answer

do I plug 9.5 for f?

anonymous · Answer

do I plug 9.5 for f?

turingtest · Answer

$$f'(x)\approx\frac{f(x+\Delta x)-f(x)}{\Delta x}$$$$f(x+\Delta x)\approx f(x)+f'(x)\Delta x$$$$f(9.5)=f(9+0.5)\approx f(9)+f'(9)(0.5)$$

turingtest · Answer

(you plug in 0.5 for delta x is the deal)

anonymous · Answer

ok so I just plug in 0.5 and multiply with 9 and I get the answer

anonymous · Answer

right?

turingtest · Answer

?
what do you think the answer is?

anonymous · Answer

4.5

turingtest · Answer

no
what is f'(9) ?

anonymous · Answer

attachment

turingtest · Answer

why do you think it's zero
no, it's given in the question

anonymous · Answer

answer is 9.5?

turingtest · Answer

no, how are you getting these answers?

anonymous · Answer

I thought I was trying to get the derivitave of f'(9)

turingtest · Answer

f'(9) is a constant, so its derivative would be zero
we don't need that, we just need the value of f(9), f'(9) and Delta x
the first two are given in the problem, and I already told you the value of Delta x

anonymous · Answer

so 0.5 x

anonymous · Answer

and then solve

turingtest · Answer

I don't know what you mean, show your work please

anonymous · Answer

what I mean is that would put 0.5 for delta then solve w/ x

turingtest · Answer

If you knew how to solve the problem you would have done it rather than explain it, it takes just a moment since I already gave you the formula above
Again, starting with the difference quotient:$$f'(x)\approx\frac{f(x+\Delta x)-f(x)}{\Delta x}$$rearranging:$$f(x+\Delta x)\approx f(x)+f'(x)\Delta x$$sub in for a particular point, and not that the difference between this point in question and the one already given is Delta x=0.5$$f(9.5)=f(9+0.5)\approx f(9)+f'(9)(0.5)$$now you have all given information

anonymous · Answer

do I still need to solve or is that the answer?

turingtest · Answer

you still need to substitute in the numbers given in the problem and do the simple arithmetic

turingtest · Answer

what is f(9) ?
what is f'(9) ?
both are given in your very post

anonymous · Answer

i got 112.5

anonymous · Answer

is that right?