Question

Find the derivative of f(x) = 9x + 5 at x = 7.
Can someone please show me a simple way to do this o_O

Answer 1

the derivative tells us the slope at any point. the function you gave is a 'linear function' i.e. its slope is the same everywhere ... :-)

Answer 2

so, in this case, it doesn't matter where you're computing the derivative -- this function yields a line hence the derivative (slope) is the same everywhere. can you figure out the slope? hint: think \(y=mx+b\)

Answer 3

@ceejays thats not correct, my options are 0,5,7 or 9

Answer 4

What @oldrin.bataku said is absolutely correct this is a st.line equation in which slope is always equal and derivative of any function tells you its slope so the derivative of f(x)=9x+5 at x=7 is 9 only\[f'(x)=9\]

Answer 5

thankyou, but im still confused on how you get that answer

Answer 6

by using the power rule:\[f(x)=9x^1+5x^0\]\[f'(x)=9*1x^{1-1}+5*0x^{0-1}=9*x^0+0=9*1=9\]

Answer 7

\[\lim_{h\to 0}~\frac{m(x+h)+b-(mx+b)}{h}\]
\[\lim_{h\to 0}~\frac{mx+mh+b-mx-b}{h}\]
\[\lim_{h\to 0}~\frac{mh}{h}\]
\[\lim_{h\to 0}~m=m \]

Answer 8

Thankyou!! <3

Answer 9

never figured the limit definition of the derivative would be considered more simple than an appeal to geometric intuition... :-P