Question

Determine this function in simplified form

Answer 1

\[\huge f(2+h)-f(2) \over \huge h\]

Answer 2

\[\huge f(x)=6x \]

Answer 3

this is definition of derivative of f(x) at x=2
first do this
\[\frac{f(x+h) -f(x)}{h} = \frac{6(x+h) -6x}{h} = \frac{6h}{h} = 6\]
then you would plug in x=2, but there are no "x's" so answer is simply "6"

Answer 4

$$\frac{f(2+h)-f(2)}h=\frac{6(2+h)-6(2)}h=\frac{6(2+h-2)}h=\frac{6h}h=6$$Intuitively, this says the slope of any secant line of the curve \(f(x)=6x\) has slope \(6\).

Answer 5

burhann how is my favourite student doing