Question

F(x+h)-f(x)

h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv

Answer 1

Answer: F

Explanation:

(i) The interval is meant to have infinitesimal width because the limit is approaching 0.

(ii) This gives the derivative at
`(x, f(x))`, which is the same as the slope of the tangent line.

(iii) False, this deals with the tangent line, not the secant.

(iv) True by definition.