Question

Show that the derivative of f(x) = 3x – 5 is f’(x) = 3. Explain in terms of slope why this is true.

Answer 1

f'(x) = (3x-5)' = (3x)' - 5' = 3 - 0 = 3.
the slope re[resents the geometric interpretation of the derivative.

Answer 2

okay there is not more information just that?

Answer 3

the slope is also the tangent of the angle formed by the graph and the ox axis

Answer 4

okay

Answer 5

i will draw it.

Answer 6

okay

Answer 7

The derivative IS the slope, so 3 makes sense is the sloe of the line, if you look at the original

Answer 8

ok

Answer 9

ignore my typos, you know what i mean lol

Answer 10

yea i got what you meant

Answer 11

y intercept (when the grapf intersects the oy axis): x=0 => y=-5
x intercept (when the grapf intersects the ox axis): y=0 => 3x-5=0 => x=5/3

Answer 12

so when you want to find the tangent of that angle, which is also the slope you get \[\tan \alpha = \frac{ 5 }{ \frac{ 5 }{ 3 } } = 5 \times \frac{ 3 }{ 5 }\]

Answer 13

which is 3. your slope.

Answer 14

okay thanks!

Answer 15

you're welcome.