Question

Conside the function f(X)=x^3-4x^2+4x.
a) Estimate the instantaneous rate of change in f(x) at x= 2.
b) What does your answer to part a) tell you about the graph of the function at x=2?
c) Sketch a graph of f(x) by first finding the zeros of f(x) to verify your answer to part b).

Answer 1

so do we have to use this formula: f(a+h) -f(a) divide h

Answer 2

Yes

Answer 3

oh ok

Answer 4

the rate of change is the slope also the first derivative
find the expression then let x = 2 to get the rate at that moment

Answer 5

ok

Answer 6

so do we have to use this formula: f(a+h) -f(a) divide h

Answer 7

@triciaal

Answer 8

when x = 0 f(0) = 0
when x = 2 f(2) = 2^3 -4*2^2 + 4*2 = 8-16 + 8 = 0
F(X) = Y
change in y/ change in x = 0/2

f(x) = x^3 -4 x^2 + 4 x
when f(x) = 0
x(x^2 - 4 x + 4 ) = 0
x(x-2)(x-2) = 0
x = 0, x = 2

Answer 9

yes?

Answer 10

so which be the answer

Answer 11

x=0 or x=2

Answer 12

@triciaal

Answer 13

the graph crosses the x-axis at 3 places approximately (-1, 0) (1, 0) and (4, 0)
maximum at (0, 4) and there is a minimum when x is between 1 and 4

Answer 14

when x = 2 y = -4

Answer 15

but at the back of the book the answer is about 0

Answer 16

x-2
(x-1)^2 -1
h = 1
what do you mean? the answer for what ?
from above we know the rate of change at x = 2 is 0

Answer 17

yep

Answer 18

here is a sketch of the graph