Question

Given a graph of f', on what intervals, is f increasing.

Answer 1

actually I don't need help on a after all. I was looking at the graph incorrect

Answer 2

I do need help on find an equation for the line tangent to the graph of f at the point (0,3)

Answer 3

I know that I am to use (0,3) for the tangent line

Answer 4

it is the f'(0) part I am confused about

Answer 5

The graph gives f'
read off the value of f'(0) = -2

you now have the slope m= -2, and a point on the line (0,3)

Answer 6

am I just looking at the point (0,-2)

Answer 7

find an equation for the line tangent to the graph of f at the point (0,3)

to do this, you need the slope of the tangent line at point (0,3)
the slope of the tangent line to a curve at x is f'(x)

In this case, look at the curve provided, which plots f' as a function of x
at x=0 we see f'(0) is -2
-2 is the slope of the tangent line to the curve f(x) at x=0

Answer 8

The usual exercise is they give you f(x) and ask for the equation of the tangent line at some point (x0, f(x0))
you would differentiate f(x) to find f'(x), evaluate f'(x0) to get the slope, and then use point-slope formula (for example) to find the equation of the tangent line.

Here, we use a graph of f' rather than differentiate.

Answer 9

yes thank you