How do you find the average rate of change of # f(x) = x^2+x+3# from [1,x]?

Answer 1

Emma Aldridge

The average rate of change of a function #f# over an interval #[a,b]# is #(f(b)-f(a))/(b-a)#.

The average rate of change of #f(x)=x^2+x+3# over #[1,x]# is

#(f(x)-f(1))/(x-1) = ([x^2+x+3]-[(1)^2+(1)+3])/(x-1)#

# = (x^2+x-2)/(x-1)#

# = (cancel((x-1))(x+2))/cancel((x-1))#

# = x+2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Alvarado

To find the average rate of change of (f(x) = x^2 + x + 3) over the interval ([1, x]), where (x) is a variable, you would use the formula:

[ \text{Average Rate of Change} = \frac{f(x) - f(1)}{x - 1} ]

Plug in the function values for (f(x)) and (f(1)):

[ f(x) = x^2 + x + 3 ] [ f(1) = 1^2 + 1 + 3 = 5 ]

Substitute these values into the formula:

[ \text{Average Rate of Change} = \frac{x^2 + x + 3 - 5}{x - 1} ]

Simplify:

[ \text{Average Rate of Change} = \frac{x^2 + x - 2}{x - 1} ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.